More than likely it does, but the answer would also depend upon just how the inverter were to be wired. I would think it very unlikely that you have an inverter and are not aware of it. Inverters are standard equipment in very few RVs. Most come standard with only a converter, which supplies 12V-dc when connected to shore power and which will recharge the coach batteries.
The only way to be completely sure would be to trace all of the wires in the RV. And inverter must be wired to be supplied from the batteries and also from the shore power or genset to recharge the batteries. They also must have an output that is wired to the batteries and one that goest through a relay device to supply the outlets desired when you do not have another source of 120V-ac.