WebDriverWait is nothing more than a (quite) fancy while/catch/sleep loop; in your particularly case you might want to replicate it yourself, for one simple reason - it polls every 500ms, which is probably too detailed resolution for this task. It also shields you from a bit more granular control.

Here's how to do the logic yourself - have a boolean variable is the user online or not; based on it's value, check is the element visible (.is_displayed()), sleep X time and repeat. An exception NoSuchElementException, StaleElementReferenceException will count as the the user offline/the boolean value false.

At the end, you're code will be pretty close to the logic in WebDriverWait - still, yours and more flexible if needed to be.

Alternatively, just pass a bigger polling internal in WebDriverWait in the current code - it's the poll_frequency argument of the call :)

WebDriverWait(driver, 28800, 5)  # the value is in seconds

I can't know where and what you've read it's bad practice to use WebDriverWait with a high number of seconds; as you see in its code it's just how much time the method is given to be running.
I presume the advice was in the tone "it is a bad practice to use WebDriverWait with a high number of seconds, because if the condition is not fulfilled in X seconds, it won't be ever fulfilled and your code will just spin and spin.". Which is actually the desired behavior for you :)

I also wouldn't worry taxing the cpu - these checks are very lightweight, nothing harmful. For this big runtime, what would worry me is memory leaks in the browser itself ;)

As for optimizing the code - what I would do is to cut on the statements repetitions; with the downside of decreasing its readability a bit. My take for the loop:

user_online = False

while True:
    # we'll be checking for the reverse of the last status of the user
    check_method = EC.visibility_of_element_located if not user_online else EC.invisibility_of_element_located

    # in the conversation page, a span with title online is diplayed when user is online.
    # the web driver will wait 8hrs=28800s for the user status to change all
    # the script will be killed by webdriverWait if that doesn't happen
    element = WebDriverWait(driver, 28800, 5).until(
            check_method((By.XPATH, "//span[@title = 'online']")))

    # The moment the user changed status
    now = datetime.datetime.now().strftime("%H:%M:%S")
    print("{} at : {}".format('online' if not user_online else 'offline', now))   # if you're using python v3.6 or more, the fstrings are much more convenient for this
    print("************")

    user_online = not user_online   # switch, to wait for the other status in the next cycle

Finally, code-wise - the script can't be left running "endlessly". Why? Because if the user doesn't change status in 8 hours, WebDriverWait will stop. To salvage that, wrap the loop body in try/except:

from selenium.common.exceptions import TimeoutException  # put this in the beginning of the file

while True:
    try:
        # the code from above
    except TimeoutException:
        # the status did not change, repeat the cycle
        pass

Writing to a file

You might want to read a bit how to do that - it's quite a simple operation.

Here's a sample - open a file for appending (so there previous logs are preserved), wrapping the while loop:

with open("usermonitor.log", "a") as myfile:
    while True:
        # the other code is not repaeted for brevity
        # ...
        output = "{} at : {}".format('online' if not user_online else 'offline', now)
        print(output)
        myfile.write(output + "\n")  # this will write (append as the last line) the same text in the file
        # write() does not append newlines by itself - you have to do it yourself

One thing that i should suggest is that in your program you need to scan whatsapp QR everytime you execute this program, just replace this line

driver = webdriver.Chrome('C:/webdrivers/chromedriver.exe')

with this

driver = webdriver.Chrome('C:/webdrivers/chromedriver.exe', options="user-data-dir=C:\\Users\\<username>\\AppData\\Local\\Google\\Chrome\\User Data\\whtsap")

this way you'll need to scan the QR but only once.