No, the press is an inherently "lighter" exercise than the bench or the incline and so you train it hard and progress it weekly.
If you are just doing some handstand work, even planche progressions, once or twice a week for a limited amount of time, you will probably be fine. However, if you really start upping the intensity with gymnastics work, you may have to play with recovery days. When I was doing a lot of gymnastics work twice a week, my shoulders were wrecked. I was working handstand/planche progressions, rings, uneven bars and pommel horse. The upside was that my press went up more than 10% in that time without me pressing even once. But, if I had been trying to run any sort of linear progression with press or bench, it may have been difficult. I was doing 2-3 hours/week total of just upper body gymnastics, though.