Hey Nick, depending on which model Inverter you have, ours also acts as a charger for the batteries. Once you have a large model hooked up, the Inverter takes the place of the stock charge controller that came with the camper.
When ever we plug ours into Shore Power, the fan comes on right away to bring the batteries up to 100%. This is totally normal and I would only worry if you dont hear the fan come on.
I know the first time we noticed this, we were a tad worried and called General RV right away. They were the ones who installed our full Solar/Inverter set-up. Once they explained it too me, I was relieved and now know that you should hear that fan come on.
The only reason I can guess it's sounding ill, like you mentioned, is usually when plugged in, it wants to charge the batteries up real fast, so you might not have ever heard the fan come on that strong before.
If we're just using the inverter while boondocking, the fan will only come on sporadically and then it never seems to be as loud as if it's plugged into shore power.
Hope that helps