If the people of Flatland didn't know they lived in a flat land, would we know if our Universe is flat?

Research is beginning to point to the possibility that at least the Level 1 Multiverse is an accurate description of the local Cosmos. And maybe there is even more, far far away in Level 2, 3 or 4 universes. Could the multiverse postulate be true, and if so, are the parallel versions flat? Why would we know we live in a flat land any more than the inhabitants of Flatland knew they lived in a flat space?