Of course having a balance chamber affects the water tolerance of regulators. And, as you mentioned, the "flow paths" (or more specifically, where the water would/could go) is different for different types of regulators. In a diaphragm 1st stage design, the HP area surrounds the balance chamber, which is filled with air at IP. If water under high pressure forced it's way into the balance chamber and compromised the o-ring seal, it would result in immediate and severe IP creep, quickly causing uncontrolled freeflow. Balance chambers use tiny little o-rings and small volumes of air, which work great when they're dry, but are much more susceptible to failure when they're wet. A very small volume of water could cause something like "hydrolock" in which case the seat would not budge unless water was forced out. In the second stage, the balance chamber is "pushing" the poppet closed with IP. If that flooded you'd have an incompressible force holding the poppet closed; the only way it could open would be to force water either out the balance chamber o-rings or back upstream through the hole in the seat. I honestly don't know exactly how that would work out in a real life situation, but I'd probably rather find out in a bucket than at depth.
The balanced piston design, and by this I mean the flow through (SPMK5 et al) design, could only send water up through the piston into the IP chamber. (and the HP port, but that;s the same in all regs) If, however, there was enough hydraulic pressure in the HP chamber, it could easily rupture the HP piston stem o-ring, which would cause an immediate and severe HP leak into the ambient chamber. The reg would still work (IP could be maintained) but you'd have a pretty nasty leak.
The unbalanced flow-through piston does not have either of these scenarios. The only place for water to go is up through the piston; as soon as IP is reached, the seat cuts off flow, shielding the piston stem o-ring from HP air.
For second stages, if you just have a simple downstream, "puck" seat design, water would go through the orifice, into the air barrel or reg body, and you be breathing water until it got flushed out; almost certainly just a few CCs. But there's nothing else it could damage.
This is one reason that the SP MK2 makes an ideal pony or stage reg; if the reg were depressurized at depth and water migrated from the 2nd stage to the 1st, you can easily just blow it back out.