Did they spend most of the time submerged?

No. In fact, overall, the boats spent the majority of their time on the surface.

When in their patrol area, they may have been submerged slightly more than they were on the surface. Early in the war, they would have been up on the surface when it was dark and submerged when it was light. However, as we became better at spotting Japanese planes and ships, some captains tended to stay on the surface longer. Since the boats were so much faster on the surface, that would give them a better chance of being able to get in front of targets.

Additionally, the transit to and from the patrol areas was done mostly on the surface.There would have been a trim dive every day, to get the boat back into neutral buoyancy. Since the transit to and from the assigned area could be a few weeks out of each patrol, mostly on the surface, the majority of the time for the full patrol is would have been spent on the surface.