Isolation transformer = floating ac inverter
I have run across two distinct and different types of 12 Vdc to 120 Vac inverters. By far the most common inverter uses a simple DC boost converter that generates about 160 Vdc. This is then fed to a full H-bridge output stage that generates 120 Vac. They call this a &quot;Modified Sine Wave&quot; inverter. In reality, it is a square-wave output with sufficient off-time that the 160 Vdc supply approximates 120 Vac.
This type of inverter will be destroyed if you ground one of the output terminals to either side of the incoming DC supply.
However, the recent 120 Vac inverters we are purchasing have a fully-isolated DC-DC converter.  Because the output of the DC-DC converter is floating, it is perfectly fine to short or connect one side of the AC output to either side of the incoming DC supply.
Note that I'm talking about Modified Sine Wave inverters in both of the above examples.
And, yes. You can safely use an AC inverter as an isolated AC supply ** SO LONG AS IT HAS AN ISOLATED DC-DC CONVERTER **