Is adding a GFCI outlet ahead of inverter as good as having one on the inverter?
If your house inverter is a true sine inverter it will work to have the GFCI outlets after the inverter, any imbalance in the hot neutral and they are I’ll trip just like with normal residential wiring you are used to.
 If the output is a modified sine wave the harmonics generated have caused problems with GFCI’s I have installed on a PV system. I did have luck with a second system back in 05? That was modified sine it did work when we tested it but I am not sure if under a heavy load the GFCI may trip like the first system did. These were the only ones the owners wanted GFCI protection many times on emergency circuits folks don’t want them to trip, I can see using them on a boat would be a good idea. Check the specifications on your inverter out put, if the graph shows a sine wave with lots of steps it is a modified sine, some of the newer ones the steps may be small enough to not cause the bad harmonics, if your inverter is pure sine it should have no problems at all.