It doesn't really work like this. The vast majority of cheaper PWM charge controllers don't measure OR control current. They control based on voltage. When the charge controller is in bulk mode, the 'switch' in side the controller is fully on and the controller acts like a wire. Once they reach absorb and float, the controller starts controlling the voltage to keep it at the absorb and float voltages.
What will most likely happen is that if your house battery is discharged, when you start the car the charge controller will turn fully on (bulk mode) a bunch of current will flow through the charge controller and you will burn out the mosfet switch inside. Alternatively, if you battery is mostly charged, the alternator voltage will not be enough above the battery voltage for the charge controller to turn on, and nothing will happen. Final scenario is that you will discover that your charge controller is 'positive ground' and actually PWMs the negative side, and nothing at will happen, not matter what.
You can use a solar charge controller as a DC-DC charger, but you need to use specific MPPT charge controllers and add a boost converter to boost the input to the charge controller up to > 17V or so. I do this with my Victron MPPT to charge a lithium battery.
That was kind of my reasoning for using the charge controller my thought was it would limit the amp draw to keep me out of trouble. I don't draw a lot of power off my house battery just a few lights and charging small electronics, I just want to keep it topped off, so I don't need a heavy duty charging system.