FM transmitter? I'm curious.
Also, does it have a 12v to 3 volt cord, or does the back of the transmitter say DC 3v? If it says DC3v, putting it onto 12 volts would not end well for it. Just wanted to check since it was a little vague.
However, on the answer, being that the transmitter only uses 3v, it sounds like its a very low power one. I don't see any power issues if you used both off a cigarette lighter plug. The only issue I could see though is the transmitter possibly feeding small amounts of RF into the power cord that could also get into the scanner. It wouldn't cause any real problems, but could cause a few more birdie frequencies with the scanner and it could remain locked on those channels during scan. The only way to see though is to try. If it does, there are easy fixes that should eliminate most of it.