Yes...If you'll notice, in the meme information there is a section with small print at the bottom that says 'meme description' and then has the text that is in the meme. This allows all memes on imgflip to be indexed, so you can simply google search it with a query like "[text you want to use] site:imgflip.com" See this search for this meme as a reference:
https://www.google.com/#q=like+a+good+neighbor+stay+over+there+site:imgflip.com
and you can see that the top 2 hits are other identical memes to this one.
You can also generate the meme, then drop it in googles reverse image search, and it will search the meme across the entire internet based on the template and text in it. Pretty powerful.