Yup, drsteve, they do and they work fine and so does mine at home, (5,000 watt gas with a compact car automotive muffler I put on it and it's nearly all enclosed so it's not loud at all, just hums), if required or wanted or the generator thingy's in both RV's (a 3400 watt built in PP Generac and an EU 2000 watt Honda) too!
Have a 2500 watt inverter with 5 group 31 12V deep cycle batteries - 225 minutes each at a 23 amp draw in the 5th wheel + 2 more of the same in the bed of the truck wire cabled with #2 gauge fine strand welder cable for both + and - to the truck's diesel engine dual alternators. All for the 5th wheel AC when not on the shore power grid. For the big Lance TC, a 1500 watt inverter and 3 of the same batteries for it, (one in the TC compartment and the 2 in the bed of the truck on the driver's side ahead of the rear wheel well and all are connected together when the TC is on. Real freedom! Some peoples idea of overkill so I've been told many times but certainly not to us and been the norm for much longer than 10 years now. Got my first inverter back in 1983, a Heart interface 1800 watt, and our inverter use had become the norm with many more for our cabined boats/sailboats and all RV's since!
Loaded for bear or what ever having lots of standalone AC power we may need or want anywhere anytime and all are right here parked at home on our property unless we are traveling and then it goes with us with either the TC or the 5th wheel.