Can you do it? Sure, but there will always be some interaction between any two antennas that are near each other. I would imagine there would be at least some detraction from the CB antennas radiation pattern, sort of like placing a large metal obect in the same place. May not affect much, but it could.
The scanner would be what I would be worried about. That CB antenna does produce energy that's going to end up inside that scanner. May not do anything harmful, but it certainly can. If both are on the same frequency, or maybe just the same band or a harmonic, the scanner isn't gonna like it much. Best bet is to put them as far apart as possible, then be careful about operating both at the same time.
It really depends on what 'close' means, a couple'a few inches, or a couple'a few yards. In this sort of case, yards are better than inches. Miles would be better than either of those two, but that's sort of ridiculous...
- 'Doc