All the commenters people saying that beta tester are doing you a favour and sending this is unreasonable are (imo) missing the point. This is a fun way to make beta users feel connected. It makes it feel kind of like beta testing for a friend.
I don't really understand why everyone is pooh-poohing this; it's just a more creative way to rate-limit their signups than relying on the usual "you are number 123 on the beta invite list".
This doesn't seem like a very reasonable idea. The entire point of beta testing is to fix bugs. The beta testers don't owe you; they are doing you a favour if anything.
it's kind of similar to beerware: <a href="http://en.wikipedia.org/wiki/Beerware" rel="nofollow">http://en.wikipedia.org/wiki/Beerware</a>