I suspect that much of the noise would be much less noticeable on GMRS vs CB since we're talking different bands. That said, whenever I've had a cb radio plugged into any circuitry that would be connected to the car's wiring harness, I get electrical noise, usually engine rpm dependent, usually from the alternator and maybe the coil packs/distributor. I typically can isolate this using a direct hot wire to the battery.

Edit: Also didn't notice it til now, but like the other commenters said, the plug you have chosen is 10 amp which won't be enough at full power. Car socket amperage is also something to consider. I've got one of these plugs which I believe the wire is thick enough for up to 25-30 amps, and comes with an in line fuse. https://www.amazon.com/CUZEC-Adapter-Socket-Terminal-CU10191B/dp/B075KF1K84/ref=sr_1_29?dchild=1&keywords=battery%2Bto%2Bcigarette%2Blighter&qid=1601343799&sr=8-29&th=1