Is it common to cite the numbers of results a search engine yields as evidence for the prevalence of something online? Is it common in academia to include the number of results a Google search on a keyword yields as an evidence for the prevalence of something online? 

I'm not intending to base my research paper on this evidence; it is just a supporting point in a paragraph.

For example, I'm writing a research paper on Stack Exchange; one of the paragraphs is about how popular Stack Exchange is in the internet. 

In one of the paragraph, I would mention that a Google search on the keyword 'Stack Exchange' yielded about 49,600,000 results, which shows how popular it is among netizens.
Do not do this. The "approximate" number of hits Google reports is completely worthless. To see why, look at this number on both the first and the tenth page of Google hits:

First results page

Tenth results page

When I just did this, I got "approximately 9,010,000 hits" reported on the first results page... but only "approximately 48 hits" on the tenth page.

Your results will probably vary, depending on your search engine bubble (another reason why this number is useless).