I wanted to have to avoid this for as long as possible, as it is an inconvenience to signups, but it looks as though I'll have to add a CAPTCHA to event signups as well.
So far I haven't had a problem with event sign-ups, just account creations.
On my site, no one can sign-up for events or post anything unless they've been moved up a rank for just this reason.
I was just having a hard time managing the accounts with all the spam ones in there cluttering it up. And trying to delete like 1000 accounts one at a time is ridiculous, so there should be an option or something to do mass-deletes.