You should be able to do one easily as long as you put fusible on the back of the t-shirts prior to cutting. I used the fusible tricot, it comes out very nice when done. Many people use the standard lightweight non-woven fusible and are satisfied with the results. With the tricot, you just have to be sure to put the stretch opposite of the stretch on the t-shirt. I loved how the fabric was very soft, not stiff when done.
The t-shirts I had to work with had prints of all different sizes. I added borders of varying sizes so that when done, all my blocks were the same size. Then I added sashing, borders and it came out great. It was heavier to handle than a traditional quilt. I didn't particularly like handling that thru my domestic machine, even with the wider harp space I have. It was a chore and I didn't quilt as much as I would have liked because of it.