ShiroKuro It may be the case that someone who is classically trained will progress more quickly in those other styles, but the reverse is probably also true
I think, for the most part, someone trained in classical piano will have a leg up. This assumes certain things, however. It assumes that they learned technique and basic ideas of musical interpretation properly step-by-step from a good teacher. Many "classically trained" pianists have just had a teacher assign them pieces, and that is usually not sufficient.
I can't see why this can not be the case. As part of classical training, I've learned the functions of each of the fingers, the wrist, the arm, coordination of various kinds to the point where you can execute difficult passages with ease. Unless someone works on the same aspects of coordination with equal rigor in a non-classical style, the classically trained person will have an advantage.