That's not how submarines work. I served on them, you get neutrally buoyant by either bringing water on or pumping it overboard. Scuba divers do the same thing (I used to be an instructor), you adjust the air in your BC to get neutral for whatever depth you're at.
Supports the jet skis travel like fish idea.
Many people with X2 remove the hood foam to fit larger engines. The air in the engine compartment gives the illusion of enough buoyancy to not sink. X2 can not float without hood foam, but they do, because of the air left in the engine compartment. They have just enough foam to slow the process to slower than the bilge pumps.
Any ski with that relies on the air in the engine compartment to not sink, but has enough foam to not go down rapidly, will work in the way SJ describes subs working. They can slowly decent as the air escapes. The rate of the decent depends on the rate of the air escaping.
So the real question is not "how far to skis sink" because that answer is most definitely "to the bottom".
The question is "at what rate do skis sink" so that some amount of estimation can be made as to how far the ski will travel during the sinking process. For an X2 with no hood foam, the answer could be hours. Skis with no foam at all can be almost immediately, and skis with proper foam could be days.
So yes, skis do kind of travel laterally like fish riding the current, except their depth only increases over time.