Could draining the hot water heater help to increase hot water pressure in the upstairs bathrooms? The heater is 7 years old.

Sediment should be drained off the bottom drain of the water heater annually... but I can't see how that can or would affect water pressure upstairs.

I would check all your shutoff valves and make sure none are partially closed.

Let me first ask a few questions and then I'll give you instructions on how to maintain your water heater. How old is your house? What material are the water pipes? Is it only thehot water that loses pressure? Cold water OK? While flushing out your heater won't increase your pressure it will prevent any more loss.
It's possible that not maintaining your heater for years has allowed minerals and sediment to build up in the heater an now it's clogging your hot water pipes on the inlet ports on the cartridges in your faucets.
For long life and fewer troubles you should keep your heater clear of mineral build-up by FLUSHING NOT DRAINING on a regular schedule. Attach a hose to the boiler drain at the bottom of the tank. With the pressure on, open the boiler drain and let it run until the water runs clear. You will see a spurt of red,(rust) followed by white or yellow grains,(lime or calcium carbonate). This shouldn't take more then a few minutes. Do this monthly to keep it clear. Now flush out your hot water lines on ALL fixtures that are affected . Now pull each aerator and clean the screens. Be sure you put them back together the same way you took them out. Don't forget to flush it out every month. Your heater will thank you for it. Hope this helps and thank you for rating my answer, Tom