I would definitely, without a doubt, remove all the texture before doing anything to the ceiling. It doesn't take all that long. However, it will be messy.
Here's what might happen if you don't remove all the texture. I'm assuming that the texture on your ceiling is original and is directly on top of the drywall. Chances are your ceiling was never primed before the texture was applied. Since the bare drywall is fairly smooth, the texture doesn't stick at all. It does, however, sort of stick to the joint compound on the seams. As soon as you apply any paint, paste or anything wet, the texture will start to bubble up and peel off. If you remove the texture, lightly sand the ceiling, and apply a good primer the finished product should look great.