If you’re trying to keep constant volume, then yes–youll need to step on the gas and give it more air.
What I found most effective for me, was getting the pitch as easy (less air) as possible to learn the shape, then working on crescendo / decrescendo exercises to build up my dynamic control on each pitch.
I had a tendency to overblow high notes, so focusing on passive air for a while helped me slay that dragon. Passive, steady constant release (not blowing).
In my opinion, its advisable to separate achieving the pitch from dynamics, FWIW.
I don’t have a sense off the top of my head at the moment how much pressure difference a low C at Forte (for example) would feel vs High C, but it’s probably relatively significant.
But I dont believe its necessary to compress the air to achieve high C. I think I can hit High C just by engaging the corners with little air. And I think Greg demonstrated that.
I’m not usually able, I think, to achieve E on the staff or G above the staff with sympathetic oscillation, but I dont believe I’m using abdominal or other compression at all, in fact I know I’m not–i can achieve those pitches with passive air.