I wouldn't be concerned about using switched power in a vehicle with a scanner radio. Considering the BCT15X draws so little current, I wouldn't consider connecting it to switched power in my vehicle. None of my HAM radios are connected to switched power. This is standard practice for transceivers since the transmitters draw a lot of current when transmitting, and there is no switched source of power to supply the required current. Best practice is to connect directly to the vehicle battery for a transceiver with a fused line of sufficient size for the maximum transmitter current draw and the length required to reach the transceiver. I have left my radios on unintentionally, and never had a drained battery after a few days because the receivers draw no more current than the receiver of a scanner radio. Often no more than 1/2 amp when actually playing a received signal through the speaker. The power supply for the BCT15X is rated 750 mA. I imagine it probably draws less than 1/2 amp when audio is present during a received signal, and probably 250 mA or less in standby.
Assuming a low capacity car battery of 550 Cold Cranking amps which has a constant Amp hour capacity of about 76 amps, and assuming a maximum constant current draw of 1/2 amp for a radio receiver, the battery would be completely drained in about 152 hours or six days.