Some dust caps are pretty effective while others are not. Some use an o-ring to seal it but thes only work if the o-ring is present.
Also if the purge button on the second stage gets depressed, the reg will flood through the second stage(s) and the presence of a dust cap is a moot point.
Soaking the reg in warm water while connected to a tank and pressurized is ideal. The idea of soaking in a rubbermaid tote on the way home sounds good - as long as the reg is connected to a pony bottle and is under pressure. Otherwise the sloshing is most likely going to depress a purge valve and allow water in the reg. Even with the pony bottle, if al the air in the pony is eventually purged, you'll have the same problem plus you'll need to VIP the tank. So if you did it, I do it where you could observe what is happening or make a fixture of sorts to hold the second stages and prevent any purging.
I disagree that first stages only need a rinse. It depends on the first stage. Some first stages allow water to enter the ambient chamber and on some of these regs it can be very difficult to effectively rinse the salt water out. A warm water soak is needed to remove both the water and any salt crystals that may have already formed.