Ambient pressure is ambient pressure and it just acts to increase the pressure exerted by the main spring to open the HP seat with the result that the IP increases by an amount equal to the increase in ambient pressure to balance the system.
IP in a first stage is determined by the pressure needed to balance spring force, the ambient pressure force and the down stream force of the air from the tank. The down stream force changes as tank pressure drops so balancing is used to ensure that the tank pressure on each side of the orifice/seat is the same so that the net effect is zero change in IP as tank pressure decreases.
Traditional balancing involved having a piston stem or balance chamber the same diameter as the seating surface, but this did not take into account the (small but still present) area of the knife edge on the seating surface itself.
Overbalancing conseqeuntly is intended to address the problem that a knife edged hard seating surface in the first stage still has a certain amount of area. This small amount of area none the less can result in a slight change (a few PSI) in IP as tank pressure drops. So to correct for this in a piston reg, the piston stem diameter is slightly smaller than the hard seat diameter. This will produce a very stable IP with virtually no change in IP across the entire range of tank pressure and more consistent performance.
In the bigger picture balancing and to a lesser extent "overbalancing" allows the use of a larger orifice in the first stage which both improves flow rates and reduces the drop in IP upon inhalation. This equates to better raw performance in terms of air flow in high demand situations and less lag time overall which makes the reg feel better to the diver.
If you go really overboard with overbalancing and further reduce the diameter of the piston stem in a piston reg you would produce a situation where the IP increases slightly at low tank pressures. This would tend to reduce cracking effort on an unbalanced second stage at low tank pressures but would have little effect on a balanced second stage. It would make a non balanced second stage breath easier at low tank pressures than at high pressures, but only at the cost of increased cracking effort at higher pressures. Again in the end, there would again be no real benefit to this approach over using a properly tuned and adjusted balanced second stage in the first place.
It is true that a higher flow rate can be achieved with a higher IP, so over balancing to achieve a higher IP at low tank pressures with a balanced second stage could result in a slight increase in flow rate. However, if this were the situation I would suspect the flow rate as being a little marginal in the first place. Thsi would be one way to get better performance out of a mediocre reg at low tank pressures but a better solution would be to use a better performing first stage design in the first place.
So a small amount of overbalancing to achieve a truly balanced system in a high perfomrance first stage is a great idea. But a claim of anything beyond that is, in my opinion, just a marketing gimmic or perhaps a means to get marginally better performance out of a compact and/or medium performace first stage design that still will not be competetive with a higher performance design anyway.
