can a power inverter be used to charge batteries for cordless tools with the vehicle off or will it drain the battery too rapidly to be useful?
Inverters are very inefficient and draw much more than they produce. They will draw a battery down very quickly.
Use the inverter when the engine is running, such as when going to the jobsite or picking up lunch. The best way is to use a 110 volt charger. Swap batteries about every 4 hours and you'll never run out.
Some cordless tool manufacturers make 12 volt chargers. See if yours does.
I know Milwaukee tools makes one.