If you're being driven by a guide, there's a chance you could see a catacomb. If you finish with the Vatican Museums and Basilica by around noon, you could stop at the Pantheon. I would grab a quick bite to eat in the vicinity, and then go on to the Colosseum. To save time, I would suggest not even going inside. Instead, walk round it on the outside, and then walk along Via dei Fori Imperiali to see the other remains of ancient Rome on both sides of the street. This might take an hour and a half, and I would guess it would be around 3 PM. If you head straight for one of the catacombs, you should have time for a visit. I would suggest the Domatilla catacomb, which is on the same side of the city, and isn't too large. However, you'll have to see which days of the week it's open.
It can all be done, but it would be very rushed. I myself, if I wanted to see as much as possible, and if a catacomb were high on my list, would also skip the Vatican Museums and instead visit just the Basilica. Then I would walk around the historic center (Pantheon, Piazza Navona, and maybe a church). Then I would just walk around the ancient Roman area and head to the catacomb. To do this, you wouldn't need any tickets at all, and you could relax a little and keep your time flexible.