Yes, yes it does.
What exact make and model inverter is installed? Does it have or can you add a real time KVA output monitor.
Basic work around would be adding a current monitoring relay to one leg of the inverter output and have it trip when the current exceeds 12.5 A(3 KW) and opens up when the current reaches some lower limit you decide.
These relays are often used on belt driven fans to determine remotely if the fan has a mechanical failure or the belt broke.
This setup will allow the load to only operate when the inverter is putting out current.
