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I've got rhe 100-400 and also the 300mm 2.8 (which is a lovely lens and easy to use hand-held). I was warned that the 500mm might be too heavy to handhold, but is lighter than the Mk1 version. I am loathe to mount it for aircraft, but I see quite a few people at airshows with the 400mm 2.8 on a tripod so it can't be impossible. Looking at the shots, apart from the lighting problems, a lot of them have what I think is camera shake - it may be that I need to try a monopod
It's not impossible to mount the lens on a tripod and gimbal. It's simply that you'll be able to capture certain shots (like low passes and approaches) more effectively, at the expense of missing most/all the shots which require significant vertical deflection. It might possibly be a personal bias, but IMHO most of the guys I see with tripods are just there to get what they can get without too much effort. They don't really want the shot.
I'd prefer a 7D with the 100-400 handheld, over a 1Dx with 800/5.6 on a tripod. Sure, those shots you do get with the tripod will be very good; but they'll be a small subset of the possibilities you could capture and you'd miss most of the show. A lot of things happen above you where the gimbal just can't see them, because you can't get down low enough, quickly enough, to frame the shot.