Trust me, the lag is there. I've got a 5SPD too. I didn't realize there was a lag until I got the tune. And it's not just a lag. Before the tune, it seems like there's more power there, but you run out of pedal. With the tune, you don't run out of pedal, only road. I'm just saying if you're on the fence about it, go for it.
I don't know that the dealer can tell if you've modified the computer, but do you really think they'd check that if they can. Plus, like you said, they'd have to prove that the computer mod made the problem. Again, it's your car and your decision, but I know that eventually you will probably do it, and you'll kick yourself for not doing it sooner. Pretty much all of us in this forum are under warranty. Plenty of us have went in for warranty work with no problem. And by the way, just because you bought the car at that dealer doesn't mean they have to perform your warranty work. You could always find a mod friendly one. But I honestly don't think it would come to that over an intake and a tune.