Yes, the way a tire is rated is "up to X load at Y max sidewall pressure" which means that it will perform as the manufacturer had tested and rated it at for mileage and performance, wet traction, braking, etc.
Tires are also considerably stronger than the ratings, especially in passenger ratings with safety factors built in. You COULD (of course not suggested!) inflate them to double the max rating and they still wouldn't fail, but there would not be any safety factor for pressure gain due to temperature rise.
I have been running with my Michelin CrossClimate2 tires (245/45/19 from my Model S) on the X at 60lbs, doing an experiment to see if there is any adverse handling or wear, and looking at the wh/mi for changes. Of course trying to find the most efficiency. This has gotten me around 415wh/mi on the highway while towing, with near zero tongue weight (about 50 lbs) and a trailer that is only around 800 lbs.
Even in winter operation in chain controlled areas in California (Donner Pass) there was no loss of traction at all, they performed perfectly. They don't seem to gain any pressure from temperature either, unless I am operating them at the sidewall max of 50 psi. Wear has been even across the tire thus far, over 15k miles on them (10k on this last road trip)
