There will probably be issues on your scanner if you key up the CB. My recommendation is to turn off the scanner if you want to transmit on the CB. I use to do this with my scanner with a 2 meter ham radio without any issues to the scanner. You would probably blow out the front end on the scanner if you did not turn it off before you transmitted with the CB.
Bruce N0JX
This will do absolutely nothing to protect the scanner.
The power switch for the scanner does not disconnect the antenna from the front end stages of the radio. It's the delicate electronics in the front end of the receiver that would get damaged from too much RF energy getting into it. Shutting off the power doesn't do anything to protect that.
If your scanner has not been damaged by the 2 meter radio, its because there is sufficient antenna separation, coaxial losses and probably a stout enough front end.
@OP:
The CB puts out 4 watts tops. Probably more like 3.5 watts. Add in the coaxial cable losses and you are probably lucky to be getting 3 watts RF out at the antenna, probably less. The coupling between the two antennas with 30 inches of spacing is probably getting very little RF into the scanner.
Jon's suggestion about the RF watt meter and a dummy load is a good one, it'll show you how much RF is getting to the antenna jack on your scanner. Truth is, unless you have a meter that is really good at reading very low power levels (as in milliwatts), you probably won't even see anything.
The other variable is how well the scanner is protected by the diodes they usually put on the antenna connection to protect the receiver.