I figure this is probably true if there was nowhere else for the pressure to go, at least in terms of water. Is this true for air pressure even considering there are other paths for the air to move closer to the blower?
A lot if things will happen because fluid dynamics is complicated.
If you reduce the opening of one register, you increase the resistance of the whole system. This increases the pressure of the whole system and reduces the volume of the whole system.
At the individual registers: The increased pressure in the whole system will cause more volume to flow out of all of the other registers (than was flowing before), because their resistance hasn't changed.
The increased resistance of the register you reduced will decrease the volume coming out of that one, but, the velocity (which is maybe what you meant by force?) will be higher, because of the higher pressure (Bernoulli's equation).
The actual degree of these effects will also depend on the system fan - as most HVAC system blowers have a very shallow pressure/volume curve (and sometimes even positive slope, yikes!), you will likely see only a very small increase in pressure and a more significant loss in volume. Nevertheless, the general relations I said above should hold. Unless you somehow push the blower into some unstable region (positive pressure/volume slope), then bad things will happen.
Always be careful naively applying the surface area relation in the cases. Going from 8" to 6" will reduce the surface area from 50 square inches to 28 square inches. Naively you could guess that this would reduce the volume to 28/50, a 44% reduction, or that it would increase the velocity by 50/28, a 78% increase, but when you consider the system, and the fan, you see that it does neither and both of these. It will decrease the volume, but by less than 44%, and it will increase the velocity, but by less than 78% (far less, in practice).
Also note that the degree to which these things happen will depend on exactly how you reduce from 8" to 6". A flat plate with high losses will make your volume loss closer to 44% and velocity increase closer to 0%, whereas a carefully designed nozzle with minimal losses will get much more velocity with less volume loss (keeping in mind that a nozzle, after all, is a device designed to convert pressure to velocity as efficiently as possible).