CB is often referred to as 11M by hams, since it occupies about that wavelength. 10M is a popular ham wavelength, and you can talk all over the world on it when solar conditions are right.
So, it wouldn't be difficult to trim a cb antenna to tune 10M. Other than that, I suppose you could use that base to mount something like a hamstick or other similar vertical antenna. Hamsticks come in many popular HF and MF wavelengths. Personally, I don't like springs on the bottom of my antennas; they make it harder to get good SWR.
If you're wanting to mount a VHF/UHF ham antenna, you'd be better off using a conventional NMO mount.
not an expert on antennas, but I would think that it should be possible to work out mounting a ham antenna on that kind of base if you keep the wiring proper. After all it's just 2 wires coming out in principle. Although the fact that the mount may be grounded to the body may matter. I would also think that it would be important to keep the length of the cable and wiring to the appropriate value for the frequency of interest. But just guessing here.