I'm curious to know if there is a place for this idea though.
There's absolutely no need to build anything at this point. Think Eric Ries' minimum viable product (http://www.startuplessonslearned.com/2009/08/minimum-viable-product-guide.html
All you need is some performer to give it a try.
Send every new connection the solicitation.
Then give out the URL from freebitcoins.appspot.com along with the performer's Bitcoin address.
If the performer gets enough positive responses (actual coin coming in), then the idea might just be a winner!
I try not to condone an idea that intentionally violates a site's terms of service but come on, ... this is ChatRoulette we're talking about, something that is a violation of nearly every rule that exists.
I like your style of putting it out there and seeing if it flies. But to get around the TOS problem, and to showcase bitcoin technology rather than just the idea of sending a performer a donation, what about this twist on the original post:
Instead of Chatroulette, the Firefox extension is built for YouTube. Since there isn't a live performer on one end, the performer's bitcoin address is instead placed by them in the first line of the description that appears under the video. The extension is able to identify this as a bitcoin address and presents the viewer with 3 options: 1 btc, 5 btc, or a text box for entering an amount with the rest of the functionality as outlined in the original post (minus the simultaneous translation feature).
This gives us an actual 'product' to market to content developers and to tech media, rather than just having a method of sending donations via the bitcoin faucet. I think it is a bit more intuitive to people/media who have never heard of bitcoin.
I realize the idea is now closer to the Chrome extension that exists elsewhere, but by including mini-wallet functionality and designing it specifically for YouTube makes marketing the tool somewhat easier.
From what I've read this doesn't violate YouTube's TOS.