You can wire the 396XT up so that it automatically powers on and off with the car (you don't need to manually power it on and off).
The 396XT 'remembers' the previous power state (ON or OFF) that it was in before power was cut as long as the batteries have been removed. In other words, you can wire the scanner's power adapter up to an ignition-switched power source, and the scanner can automatically power on and off with the car.
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As for using the 396XT as an "installed" mobile scanner, there are a few things you should be aware of before purchasing it (I assume you want the ability to occasionally use it as a handheld outside of the car. If this is not the case then I would strongly recommend you go with the 996XT instead, as it is a better choice for mobile use).
The 396XT is a well built scanner, but it's small size comes at the price of less durable physical connectors. The PCB mounted SMA antenna connector cannot handle the same amount of strain that a panel mount BNC connector can, and SMA connectors in general are not designed for frequent removal and may wear out quicker. The mini-serial data port on the side of the 396XT is a poorly designed cheap plastic connector; it is OK for occasional programming use, or permanent remote head (or GPS) hookup, but will probably wear out and/or break if connected/disconnected often.\
Also, keep in mind that the 396XT only has a headphone audio output jack. The internal audio is not powerful enough to overcome road noise, and the headphone jack is not powerful enough to drive a standard external speaker, so you must use an amplified external speaker or run the scanner audio through your car stereo.
Bottom line is: The 996XT is a much better choice for a mobile installation. It is designed for use a vehicle and since it uses the same wiring harness and mounting bracket as your BCT15, it would be a very easy "no tool" 2-minute swap out. If you insist on using the handheld 396XT then I would strongly recommend that the scanner be mounted to a piece of wood (or MDF) where you can permanently secure the coax, data, and power cables to the wood (to minimize cable/connector strain) and only remove the scanner when necessary.
P.S. The RH96 does indeed work with the 396XT. I can control almost every function (everything except power). The only thing it will not do is flash the backlight for priority channels like the scanner itself will, and you are limited to just a plain orange backlight color. (NOTE: the RH96 will flash the backlight when connected to a 996XT, but it won't do it when connected to a 396XT. I have no idea why, as both scanner models support this feature on the actual scanner itself).
Whatever you decide, good luck and happy [mobile] scanning
