The simple answer is yes - it is of course possible to become a trained professional musician without any study of jazz. There are various extremely successful keyboard players who did not come from a jazz background - take Rick Wakeman, for example.
You will slightly limit yourself if you explicitly avoid jazz, but it is not absolutely necessary.
The reason I say this is that jazz has had an influence on almost every genre of current music, so no matter what you do you will pick up bits of jazz technique without even being aware of it.
I am not a huge fan of jazz myself - I cope with blues-jazz, but I have trouble deciphering some of the atonal/arhythmic modern jazz styles. I do, however see the value in trying to learn at least the basics - the direct benefits are some alternative changes when soloing (as I'm a lead guitarist this helps my repertoire) and potentially a wider range of session work I can get paid for. As I learn more of other styles of music I find myself able and wanting to try more avenues, so jazz is creeping in more - and you may find the same happens :-)
update I attended the Edinburgh Guitar and Music Festival this weekend, and had the privilege of attending a seminar by Hugh Burns (played the guitar on Gerry Rafferty's Baker Street, George Michael's Careless Whisper and many others, and has made a good living as a session musician since the 70's.) The topic was 'Making it as a session musician'
His guidance was that while you didn't need to cover all genres, the more you knew the better your opportunities for work. And being able to read music was a huge differentiator for him. He also said that the greater part of his skill came from playing with other skilled individuals, so although he went into session work with some training, what counted was enthusiasm, ability to learn, and just playing with others.