Tiny210v2 battery backup

I'm planning on purchasing one of these boards to use as a car pc, Is it
possible to connect a battery pack to this board so that when the car is
switched off it remains running for a set period of time and when on power
it will charge the battery?

Should be pretty straight-forward to do this.

Do you only want to charge your external battery pack when the car is
running? You can get or design a buck converter that will draw microamps
after the battery charging cycle is finished. So, you could have the
charger attached to the car all the time.