How "ugly" is the ceiling? Texture hides a lot of faults, but not all of them. You might consider going back and dressing up the ceilings with a top coat of compound to smooth everything out. It's amazing what a pro can do with a mud box.
What kind of texture are you considering? Do you think you will be spraying on the texture or hand applying it? How big of an area are you considering doing? How much help will you have at hand?
Trying to focus on the ceiling during a texture job means you shouldn't have to worry about trip hazards around your feet. Move everything out of or to one side of the room, texture the empty side, quickly have you helpers move everything to the finished side and continue to finish the remaining ceiling before the edge of your texture starts to dry or you will see where you stopped and started the halves. Be sure to cover your flooring under your work. Expect some splatter on the adjoining walls.