The question is could your legs take it. A road style hybrid or cyclocross would be a better choice for long distance riding although there are mountain bike riders here on the forms who have toured with their mountain and mountain hybrid bikes long distances. It's more of a workout for your legs, that's for sure and definitely not as fast as a road bike but the gearing is appropriate for just about any type of terrain. Naturally slicks will roll faster and better on paved surfaces than knobbies. A road hybrid will do nicely off road but not for anything as aggressive as hopping curbs or riding down stairs. The cyclocross may not be a good choice for that kind of off road riding either but I honestly have little knowledge of these bikes.
It sounds like you either have to get a road bike AND a mountain bike or decide just how aggressive you want your off road experience to be.