Can you build underwater cities in Spore?

No. You have very little control of where your cities are built until you reach the space stage. Even then cities are limited to relatively clear, flat areas of dry ground which must be placed by spice vents.

EDIT: However, there was a planned "Fish Stage" and one could elect to remain underwater, and build underwater cities in space stage, and Maxis is considering adding that option in a later expansion.

+ to EDIT: "Fish stage" was actually supposed to be a portion of the creature stage, but then the control would be much harder and like space stage, so it was cancelled. Also, you could not choose to stay underwater.