Several people have done denim. The laser damages the threads in a fabric. Denim is a heavy fabric so you can do a little damage and no big deal. I suspect the problem with a t-shirt is that the lighter material won’t weather the laser as well and your settings would need to be dialed in perfectly. If it will work at all.
If you don’t have to laser the t-shirt, you can make a stencil and use fabric paint. I recall a couple different methods including making a “silkscreen” from mylar. I think this would be the way to go with t-shirts.