Though Pumpkins are shallow rooted, I wouldn't expect it to do well in only 4 inches.
That's extreme shallow.

Why only 4"? Whats under the 4" of soil? 4" inches of soil won't hold much moisture either and pumpkins love their water.

I could be wrong here, but I don't see it turning out well.

I think Bruvyman is right, 4" very shallow. However, can you build up mounds or hills on the 4" surface? That might get you the depth you need.