Yes, mechanical compression ratio is a determining factor in both heat and pressure. That's why engines with superchargers are almost always built with a lower mechanical compression ratio.
The more you compress a gas, the closer it becomes to liquid form. You cannot compress a liquid. A denser gas will approach a liquid state faster during compression and yield a higher pressure.
Keep in mind, while MWA, or any variation thereof, will lower the temperature of the intake charge, making it more dense at the same pressure, the temperature of the cylinder, the piston, and the combustion chamber will not be lowered appreciably, when the cooler, denser intake charge reaches the cylinder, it will rapidly absorb that heat, and reach a temperature nearly the same as the intake charge would have been had it not been cooled by the MWA.