Can running both elements of a water heater at the same time increase pressure?
The unit is absolutely NOT designed to run with both elements on. This will void any warranty or safety standards of the unit. For the plumber, or anyone else, to suggest this is ok is EXTREMELY irresponsible.

Besides, while running both elements will heat the water up faster, it will not likely increase volume by much. To increase the volume, you need to......increase the volume. IE: bigger tank.