I come from the other direction - musician (with qualifications and things) who wants to be a pilot and is having to do some educational backpedalling to do it, so I've thought about this a lot. Both are in the 'dream career' category, but the sort of people who actually manage to get into either seem quite similar - maybe you could say childlike, but who cares? No one sneers if you actually manage it and to do that you have to be bold.
Lots of musicians are hobby pilots and vice versa, but I think it would probably be harder to juggle the two professions. Performing is one of the few occupations which is as tough to get into and as hard work to keep going as flying seems to be; you need to be able to accept gigs whenever they are offered to you if you possibly can - and to be wide awake for them.
But I don't believe it would be impossible to do - it might work quite well if you could pull it off. A steady flying job which keeps the money coming in and fitting in gigs/writing/rehearsals around it, as there is more freedom involved there. You are not then constricted by the need to earn (most musicians have to do a bit of teaching or something on the side) and may find you are able to fulfil those creative urges as a result. Lets face it - most bands that start off with the intention of becoming famous fold. But it would be a pretty fine(/knackering) life if you could fly by day and spend your nights off playing to an enthusiastic group of followers on the London circuit (or whatever you equivalent is).
Finally, I have always thought it's a shame that in order to follow a career and earn a living, people with different facets to their personality and a set of diverse aptitudes are forced to frustrate parts of themselves.
I'm a classical musician, which is a bit more rigid unfortunately, but I'm certainly keeping my options open.
