Just based on what's happening when tow/haul engaged, I would answer yes to some degree. But mainly it's holding gears longer, downshifts under breaking, shifts much firmer, and engages TQ lockup sooner, and remains locked through some gear changes. It would take higher line pressures to do so, but we're talking about a computer controlled transmission. So line pressures are increased to lock the TQ, and make the shifts.
But here's a quick lesson in auto trannies. There are no gears changing. All the gears that are in a transmission are already engaged. Meaning teeth on teeth all the time for every gear in the case. What's in a transmission that "changes gears" are metal bands that wrap around a "drum" that is full of gear and clutch packs. Solenoids engage those bands. When you are missing a gear or can't hold a gear it's because that band is worn, and isn't grabbing hard enough. The increased pressure would only be to hold the band tighter, or shift quicker. Some programmers (Edge) increase overall pressures, so the bands will grab harder based on increased HP and Torque trying to overcome that grabbing force of the bands. (Simplified explanation)
The quicker firmer shift of tow/haul is to help decrease friction, and in turn reduce heat (smooth shifting auto trannies are bad news). Hauling a big camper means more work, and those smooth shifts with a heavy load create more friction during shifts and more heat. It's the same reason to lock up the TC earlier, extend the life of the transmission by reducing friction wear and reduce temperature. Also, exhaust braking without a locked up TQ will generate a great deal of friction/heat. Since the transmission is programmed to downshift and "compression brake" in tow/haul, line pressures lock the TQ.
So yes, some line pressures are increased, but it's not a simple, "Well they go from 15psi to 50psi". The pressures are always adjusting based on conditions, and certain conditions may call for pressure, or just call for that pressure sooner.