Per FCC rules, yes CB radios can be controlled remotely. BUT, they must be hard wired and not wireless control.
§95.419c (CB Rule 19)
(c) Remote control means operation of a CB transmitter from any place other than the location of the CB transmitter. Direct mechanical control or direct electrical control by wire from some point on the same premises, craft or vehicle as the CB transmitter is not considered remote control.
Is there similar or same rule in Europe like USA has? Then yes, a USA radio can be controlled hard-wired remotely. Even a computer with wires to the radio for control would work. A computer with a phone patch wired to a CB radio with phone patch will work. no wireless. BUT, if different in Europe, follow those rules.