I've seen more times that not scanners and commercial radios alike get toasted because of putting 2 radios, or scanner and radio on the same antenna and connecting them by a "jumper".
The only exception I've seen to this rule is using a dual band V/UHF antenna and using a splitter made for using one antenna with 2 radios. Maybe they make something like that for CB's but those aren't my thing so I'm not sure. If you run them off the same antenna it may not affect the scanner right away but I feel certain that over time (shorter rather than longer) it will eventually roast, meaning desense, the front end of the scanner.
And there's a lot of times I can say that I'm a gambling man but when it comes to my $500 radios that is one place that I don't gamble.