I cannot give you a definitive answer, Louise, but I doubt it. A cake filled with strawberry preserves does not require refrigeration, but the open jars are usually kept in the refrigerator.
I agree with Sandra, although I don't really know what a strawberry filling that comes in a sleeve is!
Thank You All! I already made the cake, and just to be safe, I did refrigerate it. But I'll remember this for next time.