I have a 400watt inverter in my work van, use it to power battery chargers for my grease gun, impact and a light wand.
I HAVE used it to run a 1/2" drill, it didn't like it and I ended up blowing a 15amp fuse for the circut it was powered from (go figure) It was an act of desperation. the drill would only run with the trigger pulled all the way, would not run as a variable speed. All of which I pretty much expected.
A larger inverter would have probably worked better, but the speed issue would have been the same.
I have found some battery chargers don't like inverters, as many inverters don't supply a true sine wave power flow. but a modified square wave, some circutry can't handle it.
I want to add a 1200watt inverter and a second battery and isolator to the van, but I need to figure out the charging system on the Sprinter first. Fawkin Mercedies does some weird shit.