I agree with GailG, wonder under will work but it leaves the applique stiff. Additionally, you will have to use a pressing cloth when you fuse as most T-shirt imprints will melt when hit directly with a hot iron. If she has any T-shirts that have a rubbery imprint, you can't use it. The rubber stuff can't take the heat from the iron and it kind of puckers/wrinkles up.
Also you may wish to consider the recipients wishes. While your idea sounds cute, you could lose a lot of the imprints by cutting into odd shapes and they may have special memories of these events and don't want dates/cities/name of event etc lost.
Edited to add, why don't you try the shadow box setting instead. Not many T shirt quilts are done this way and it adds a lot of interest, as does cutting them into different sizes like this quilt:
[ATTACH=CONFIG]525395[/ATTACH]
Last edited by feline fanatic; 07-17-2015 at 12:06 PM.