I don't know about doing quilt-as-you-go on a t-shirt quilt, but I do know that most t-shirt quilts have quilting around the logos of the t-shirts. There would be too much unquilted space without it. Some people just do all-over meander quilting, even over the logos, so that is a possibility too.
Edit: Here is a link to a company that makes t-shirt quilts for people. You can see on the photo that they used an all-over close quilting pattern on that quilt. The ones I have seen displayed at quilt shows, made by people in their homes, all had less quilting -- either a large meander, or quilting around the logos and in the sashing strips.
Regarding quilt-as-you go, my concern would be bulk in the joins and also covering up all those joins afterwards. I think most t-shirt quilts are done the traditional way. However, a combo approach might make it easier -- that is quilt a row at a time, then join the rows.
Last edited by Prism99; 01-26-2014 at 10:42 AM.