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This answer mentions,
The single most effective thing you can do to improve your acclimatization rate is to get in good aerobic shape before starting your trip.
It seems plausible that being in good aerobic shape would help one acclimatize, are there there any studies to back this up?
No - the studies show that aerobic fitness has no protective effect. This is from the Institute for Altitude Medicine:
MYTH - PHYSICAL FITNESS PROTECTS AGAINST ALTITUDE SICKNESS.
Physical fitness offers no protection from altitude illness. In fact, many young fit athletes drive themselves too hard at altitude prior to acclimatizing thinking they can push through the discomfort. They ignore signs of altitude illness thinking it can't affect them because they are fit and healthy. Everyone, regardless of fitness, is susceptible to AMS.
Anecdotally, I remember a season in Chamonix with my climbing partner - we hadn't done much training before the trip but spent a few days acclimatising. Then we were joined by a couple of friends who were superbly fit, having recently run fast times in the London Marathon. We blew them off the hill for the first two or three days till they caught up with their acclimatisation. There are no shorcuts.
