Frank, in part it depends on what you are calling high/low spots. In many older homes where the ceilings have since been sprayed it was done in part to help hide the fact that the ceiling joists are no longer flat and the ceilings waver up and down. This you will not remove by retexturing.
But, newer style acoustic texture is a finer material, and will give you a fresh, clean finish that's not as "heavy" looking as the textures of years past. If you have it resprayed, the existing texture needs to be scraped down. (Not necessarily completely removed, but knocked down and smoothed)
LJ is correct about going back to a flat ceiling; it's usually a large amount of work, and you're likely to find it was textured for a reason (hiding imperfection). If at all possible, I'd have this work done by a drywall contractor with spray equipment; most roller applied ceiling textures do not come out looking even and I think you'd be disappointed.