Not exactly. 12V static from the drill battery a little more static
from the car battery (most will be about 13V) then put the drain on them.
The drill battery is likely to drop down to like 9 Volts quickly (internal
resistance) but the car battery may only drop down to 12V. That
difference could burn a motor that was not designed for it.

I have a cheap 12V drill that is interchangeable with a 18V power pack. No
problems so far, but I don't use it much either.

Voltage drop is huge on a 12V system and if anything should be ok for a 12V
drill. I use #4 cables from the 12V battery to the car power amp for the sub
woofers - less than 10' of run at that, and mostly for voltage drop.