Yes, I love t-shirts (I own over 160) and I know that a lot of people really love free stuff. As others have said there are issues like what if someone misrepresents a brand, but ignoring that I think the idea is fantastic.

If you market it well (I would suggest aiming at end of high school / start of college age people) it could really take off. I don't think posting it here will get you much useful feedback, the HN demographic aren't really the sort of people this will appeal to.