They'll react the same way as if they were in the next socket on the wall. So that's no reason not to use an extension.
If I plug something in which causes the plug-in solar to not disconnect in the required time then it would matter.
I can guess how the plug-in solar detects disconnection, but it is only a guess.
So lets say for example I have a grind stone plugged in, the weight of the stones will keep it revolving for a little time, and the back EMF can give you a nasty shock if you touch the plug before it has stopped revolving, but likely they will not revolve for too long, so one would need to be quite unlucky to get a shock from the plug, but if that back EMF causes the plug-in solar inverter to think it is still connected, it may extend the time.
Either it would cause the voltage to raise until 253 volts is reached and then turn off, or it could delay it until the voltage has dropped to 216 volts, before turning off, could extend the time before the extension lead plug is safe to touch. It may detect the speed out of range, but the idea is that a solar array will shut off fast with loss of grid but not with just a dip in the grid, if a large load coming online auto-disconnected all solar inverters, it could cause a chain reaction and loss of whole grid.
We have seen the experiments, with both high and low loads, and although it will decay fast with a high load, it has been found low loads specially rotating loads, can delay the turn off.
This is where experiments by the likes of efixx can give one a false sense of security, one would not expect anything else but it to disconnect with a SDS drill in parallel, but what about sheep shearing clippers sharpening disc, I remember the clippers would stall our generator, but if we ran the sharpening disc first, this would allow the clippers to start up without it causing the generators field to collapse.
The real problem is, we simply don't know what would happen.