Will:
Yes....mostly. Lower pressure at the barrel muzzle typically means less noise produced at the muzzle end of the suppressor, but the design of the suppressor baffles, spacing, clips, and aperture diameters can also factor in to have a slightly opposite effect.
Remember that suppression is really about thermodynamics instead of simply time-delaying a sudden release of high pressure gas. The time delay increases the amount of thermal energy transferred to the suppressor itself, gives the gas room to expand a little and lose heat energy before bleeding the remaining pressure to equilibrium with atmosphere. Following that train of thought, if your suppressor is built to deal with lots of very hot, high pressure gas, then of course it will be most efficient when fed enough volume and pressure. Less going in can actually make it louder because the cross-jetting efficiency is below optimum and a relatively cool, slow-moving, small puff of gas just goes straight through it like poop through a goose.
A perfect example of less not being less is one of the Gemtec .308 suppressors which only has a multi-chamber muzzle brake, a center baffle, and an exit baffle but has some insanely complex clips. It is very efficient and bare-ear cozy with full power ammo even when quite hot, but is also uncomfortably loud with the mildest subsonic loads using low-volume pistol powder.
If your suppressor is efficient at stripping and trapping low-pressure gas (such as K-baffles and well-designed hybrid-clip, 50⁰ necked baffles), then minimizing muzzle pressure by using a powder that dumps most of its energy into the brass, barrel chamber, and bullet will put less load on the suppressor and be more quiet.
