You would think. Those of us who have been wasting time on the internet for long enough remember the Secret Crush Meme from LiveJournal [1], which worked just like this. It was great up until someone realised they could just say they had a crush on everyone they knew to get a list of who had crushes on them, without any genuine reciprocity of the crush.

If you could figure out a way to make it somehow costly to falsely say you have a crush on someone, this might work, but until then, this is game-theoretically wince-inducing.

[1] https://en.wikipedia.org/wiki/Anonymous_matching