I don't think the lightness of "dry-wick" fabric is an issue. Weight of a fabric doesn't necessarily guarantee strength (or lack of it weakness). The fiber content of these fabrics is usually polyester, which tends to be stronger than cotton. My concern would be whether or not the fabric will "pill" or get pulled threads (which is a characteristic of threads that are knit rather than woven). Honestly, I wouldn't sweat using this shirt in a t-shirt quilt (pun intended,
).
If you are concerned that the weight of this fabric is too light compared to the weight of the other fabrics in the quilt, you could back it with a heavier weight fusible than the other fabrics get. A fusible tricot, for example, would add a lot of body. There's no rule that you need to use the same weight fusible on every fabric.