Using a 12V Li-ion battery temporarily while charging the original

I have a situation here where I plan to use a 12V Li-Ion battery to replace the 12V one while I charge up the 12V battery at home with a regular car charger. Because I am unable to lock the car when the 12V battery is taken out, I am worried about the car being stolen (I do not have a garage, as I live in a flat). I have tried to test unlocking the Prius C driver's door with the car key, but it doesn't work when the 12V battery is disconnected - it locks alright, but I can't unlock it.

So my bright idea is to connect a 12V 10AH Li-Ion battery to the car when I take out the 12V car battery for charging. The car will NOT be driven during the time I am charging it, and the Li-Ion battery is just to power the car doors and a little more (aftermarket car alarm only, no hard-wired dashcam). Would this reasonably feasible?