Yes, definitely. How much luggage would you have? I'd probably book a hostel dorm bed for the day (will come in handy if you want a shower, and you can store the luggage in the hostel's luggage room) and the cost will be in the $10-15 USD range. Hostel Catedral is a super-central possibility.

I'd take a prepaid taxi into the area around the Zocalo (where Hostel Catedral is), drop off my luggage, and set off on a walking tour around this area. You should have a good map, of course.

Depending on your interests, you could easily spend hours or days here, but you could also head off to the anthropology museum, which is most impressive, in Chapultepec park, or the modern art museum, also in Chapultepec park, or any other of numerous destinations. I took the subway, but if you figure out how to take a safe taxi, you could do that too.

You'd have time for lunch somewhere. So get a guidebook, and a map, and you can figure out a good day for yourself.

I would head back for the airport earlier than you'd expect to need to do so, because the traffic could be terrible (I've never done this route at a super-busy time, but I know it can be bad).