Short answer: Yes

One way to achieve what you want (that works for my package) is:

1. Store the packages snippet definitions in two text files somewhere in the packages inst/ directory. It's important that the snippets follow exactly the formatting rules (e.g. tabs at the start of the lines, not spaces). I have one file for R code snippets and one for markdown.

2. Define a function that reads these files and copies their content into RStudios user snippets files. These files are generated at the first attempt to edit the snippets (Tools -> Global Options -> Code -> Edit Snippets) (I think RStudio uses an other, not user exposed file before one tries to edit, not sure though). On ubuntu the RStudio files are called 'r.snippets' and 'markdown.snippets' and are in '~/.R/snippets/'. I also check if the snipped definition already exists, and double check the tabs at the start of the lines before using cat(..., append=TRUE) to add the packages snippet definitions.

3. I first used an elaborate .onLoad function with configs and all but now I just export a addPackageSnippets function ;)

Edit

Some code:

Part that checks for already existing snippet definitons: I just read the rstudio file and extract the lines starting with 'snippet'. I do the same for the packages snipptes definition file and use setdiff (one might want to also use trimws on the lists, just in case there is some trailing white-space)

# load package snippets definitions
#
pckgSnippetsFileContent <- readLines(pckgSnippetsFilesPath)

# Extract names of package snippets
#
pckgSnippetsFileDefinitions <- pckgSnippetsFileContent[grepl("^snippet (.*)", pckgSnippetsFileContent)]

# Extract 'names' of already existing snitppets
#
rstudioSnippetsFileContent <- readLines(rstudioSnippetsFilePath)
rstudioSnippetDefinitions <- rstudioSnippetsFileContent[grepl("^snippet (.*)", rstudioSnippetsFileContent)]

# find definitions appearing in packageSnippets but not in rstudioSnippets
# if no snippets are missing go to next file
#
snippetsToCopy <- setdiff(pckgSnippetsFileDefinitions, rstudioSnippetDefinitions)

For context here is the whole 'addPackageSnippets' function. The function is using only the base package, except getOS which returns one of 'linux', 'windows' or 'mac' (i.e. a wrapper around Sys.info()

#' @title Export snippets
#'
#' @description \code{addPackageSnippets} copies all (missing) snippet definitions
#'   in 'inst/rstudio/Rsnippets.txt' and 'Rmdsnippets.txt' to the RStudios user snippet location.
#'
#' @return boolean invisible(FALSE) if nothing was added, invisible(TRUE) if snipped definitions were added
#' @export
#'
#' @examples \dontrun{addPackageSnippets()}
addPackageSnippets <- function() {

  added <- FALSE

  # if not on RStudio or RStudioServer exit
  #
  if (!nzchar(Sys.getenv("RSTUDIO_USER_IDENTITY"))) {
    return(NULL)
  }

  # Name of files containing snippet code to copy
  #
  pckgSnippetsFiles <- c("Rsnippets.txt", "Rmdsnippets.txt")

  # Name of files to copy into. Order has to be the same
  # as in 'pckgSnippetsFiles'
  #
  rstudioSnippetsFiles <- c("r.snippets", "markdown.snippets")

  # Path to directory for RStudios user files depends on OS
  #
  if (getOS() == "linux") {
    rstudioSnippetsPathBase <- "~/.R/snippets"
  } else if (getOS() == "windows") {
    rstudioSnippetsPathBase <- file.path(path.expand('~'), ".R", "snippets")
  } else {
    warning(paste0("goSnippets() is only implemented on linux and windows"))
    return(NULL)
  }

  # Read each file in pckgSnippetsFiles and add its contents
  #
  for (i in seq_along(pckgSnippetsFiles)) {

    # Try to get template, if template is not found skip it
    #
    pckgSnippetsFilesPath <- system.file("rstudio", pckgSnippetsFiles[i], package = "myFunc")
    if (pckgSnippetsFilesPath == "") {
      next()
    }

    # load package snippets definitions
    #
    pckgSnippetsFileContent <- readLines(pckgSnippetsFilesPath)

    # Extract names of package snippets
    #
    pckgSnippetsFileDefinitions <- pckgSnippetsFileContent[grepl("^snippet (.*)", pckgSnippetsFileContent)]


    # Construct path for destination file
    #
    rstudioSnippetsFilePath <- file.path(rstudioSnippetsPathBase, rstudioSnippetsFiles[i])

    # If targeted RStudios user file does not exist, raise error (otherwise we would 'remove')
    # the default snippets from the 'user file'
    #
    if (!file.exists(rstudioSnippetsFilePath)) {
      stop(paste0( "'", rstudioSnippetsFilePath, "' does not exist yet\n.",
                   "Use RStudio -> Tools -> Global Options -> Code -> Edit Snippets\n",
                   "To initalize user defined snippets file by adding dummy snippet\n"))
    }

    # Extract 'names' of already existing snitppets
    #
    rstudioSnippetsFileContent <- readLines(rstudioSnippetsFilePath)
    rstudioSnippetDefinitions <- rstudioSnippetsFileContent[grepl("^snippet (.*)", rstudioSnippetsFileContent)]

    # replace two spaces with tab, ONLY at beginning of string
    #
    pckgSnippetsFileContentSanitized <- gsub("(?:^ {2})|\\G {2}|\\G\t", "\t", pckgSnippetsFileContent, perl = TRUE)

    # find defintions appearing in packageSnippets but not in rstudioSnippets
    # if no snippets are missing go to next file
    #
    snippetsToCopy <- setdiff(trimws(pckgSnippetsFileDefinitions), trimws(rstudioSnippetDefinitions))
    snippetsNotToCopy <- intersect(trimws(pckgSnippetsFileDefinitions), trimws(rstudioSnippetDefinitions))
    if (length(snippetsToCopy) == 0) {
      # cat(paste0("(\nFollowing snippets will NOT be added because there is already a snippet with that name: ",
      #            paste0(snippetsNotToCopy, collapse=", ") ,")"))
      next()
    }

    # Inform user about changes, ask to confirm action
    #
    if (interactive()) {
      cat(paste0("You are about to add the following ", length(snippetsToCopy),
                 " snippets to '", rstudioSnippetsFilePath, "':\n",
                 paste0(paste0("-", snippetsToCopy), collapse="\n")))
      if (length(snippetsNotToCopy) > 0) {
        cat(paste0("\n(The following snippets will NOT be added because there is already a snippet with that name:\n",
                   paste0(snippetsNotToCopy, collapse=", ") ,")"))
      }
      answer <- readline(prompt="Do you want to procedd (y/n): ")
      if (substr(answer, 1, 1) == "n") {
        next()
      }
    }

    # Create list of line numbers where snippet definitons start
    # This list is used to determine the end of each definition block
    #
    allPckgSnippetDefinitonStarts <- grep("^snippet .*", pckgSnippetsFileContentSanitized)

    for (s in snippetsToCopy) {
      startLine <- grep(paste0("^", s, ".*"), pckgSnippetsFileContentSanitized)

      # Find last line of snippet definition:
      # First find start of next defintion and return
      # previous line number or lastline if already in last definiton
      #
      endLine <- allPckgSnippetDefinitonStarts[allPckgSnippetDefinitonStarts > startLine][1] -1
      if (is.na(endLine)) {
        endLine <- length(pckgSnippetsFileContentSanitized)
      }

      snippetText <- paste0(pckgSnippetsFileContentSanitized[startLine:endLine], collapse = "\n")

      # Make sure there is at least one empty line between entries
      #
      if (tail(readLines(rstudioSnippetsFilePath), n=1) != "") {
        snippetText <- paste0("\n", snippetText)
      }

      # Append snippet block, print message
      #
      cat(paste0(snippetText, "\n"), file = rstudioSnippetsFilePath, append = TRUE)
      cat(paste0("* Added '", s, "' to '", rstudioSnippetsFilePath, "'\n"))
      added <- TRUE
    }
  }

  if (added) {
    cat("Restart RStudio to use new snippets")
  }

  return(invisible(added))

}

For anyone who comes across this thread, and to add to Dario's great answer: from RStudio v1.3, the filepaths have changes. So in his function, the section for setting rstudioSnippetsPathBase would need to change into something like the following

if (rstudioapi::versionInfo()$version < "1.3") {
    rstudioSnippetsPathBase <- file.path(path.expand('~'),".R", "snippets")
  } else {
    if (.Platform$OS.type == "windows") {
      rstudioSnippetsPathBase <- file.path(Sys.getenv("APPDATA"), "RStudio", "snippets")
    } else {
      rstudioSnippetsPathBase <- file.path(path.expand('~'), ".config/rstudio", "snippets")
    }
  }