I tried to use an overleaf url, and it didn't work, so no, it doesn't already exist (because the overleaf pages are very fancy html with tutorial popups and so on basically).
I also think it'd be pretty cool
Support told me dropbox was the way to go for urlminding LaTeX, so I tried it - I put a symlink in my local dropbox folder to my actual .tex file, it auto-syncs, and I give beeminder the dropbox link. It definitely works quite all right [EDIT : actually, with a symlink, maybe not so right after all as it didn't seem to update today. Poking around more now...] so, it'd be lovely, but it's not really an issue for me that it doesn't exist. I don't use overleaf that much, tho.
Regarding your comment, pro-tip : words are 5 characters long, so 2500 characters is 400-500 words. And of course more configurable options are always nice to have, methinks