Try-catch short-circuit/fall-through java

I want to use a try-catch block to handle two cases: a specific exception, and any other exception. Can I do this? (An example)

try{
    Integer.parseInt(args[1])
}

catch (NumberFormatException e){
    // Catch a number format exception and handle the argument as a string      
}

catch (Exception e){
    // Catch all other exceptions and do something else. In this case
    // we may get an IndexOutOfBoundsException.
    // We specifically don't want to handle NumberFormatException here      
}

Will the NumberFormatException be handled by the bottom block as well?