Can I replace my bathroom's floor tile before replacing the tub?
Sure, but the problem is that you don't know that the new tub will be exactly the same width. Usually flooring is one of the last things completed in a bathroom remodel. 

If your current tub is fiberglass (and not cast-iron) you may be able to cut out the lower portion of the face to allow you to run tile underneath for a short distance. You'd then install your new tub above tile level, using filler plywood or whatever.