LMB

I am making a t shirt quilt for a friend who is very ill. She collected Notre Dame T shirts and wanted a quilt made for her sofa. The problem I am having is that I have never made one. I have all the pieces cut out, have picked the backing and border fabric, and and want to put it together. I could make it plain and stitch in the ditch... but do I also quilt the t shirt part (the inner squares with the pictures)????? I would love to do quilt as you go... but am totally confused about this. I backed the t shirts with a lite fusible web to help hold the shape... does that mean I can quilt around the pictures or would I be inviting trouble by trying to quilt on the t shirt part? Thank you so much, as I know you are the best quilters around and if anyone would know... you will.
Linda