Not a stupid question - I continue to learn/relearn this stuff.
If you are off shore power and using 12v DC things (fans, lights, TV, etc.), you should not need to turn off your Go Power Inverter Charger (GP-IC) while using solar to charge/use your battery.
While unlikely, if your solar charge controller (manages solar charge going to batteries) has been integrated into the (GP-IC) energy management system (EMS), then turning it off may also prevent the battery from being charged. Is your solar controller also a Go Power product?
Irrespective, you would, however, want to keep an eye on battery discharge, particularly if you are using a lead acid battery, to ensure charge does not go below 50% capacity.
Is this your GP-IC?