I don't know. What display do you have, and what is it's video response time? I think it depends on the response time as I have played 360 on my LCD monitor at home, which was probably around 12ms and I got a LITTLE bit of lag. However playing on my current monitor with 3ms response time, I get no lag. But this does look like a good add-on. I might sell my Canopus ADVC110 for this...
Edit: I don't think the EveTV itself will cause any lag
It will work on the iMac as long as you have an open USB port. But as far as quality goes, I'm not sure. I'd have to test it out in person. I've read a lot about people wanting to use there iMacs to game, and running games off your 360 would be easier. I say you're okay, but it seems like your looking for a solid reply. But I found this somewhere on these forums
Edit: found on link: "I have the EyeTV 250 and can confirm that the game mode is completely lag free when hardware encoding is switched off. I've only tried it with my Gamecube"
And here is another link saying it has a little bit of lag
I have the EyeTV 250 and I've played Gran Turismo 4 on my 23" ACD with it. It had a slight amount of lag which would matter in very tough and fast-paced games, such as GT4. But, for many others, it really wouldn't.