Your question was "
CAN I use a GFI?" There is never a time when you cannot use a GFI. The only question is what you expect it to do.
One of the unfortunate things about a Ground Fault Interrupter is the inclusion of the word "ground" in its name. It implies that a GFI MUST have a ground connection in order to work. Not so. A GFI simply compares the amount of electricity flowing out of the source through the HOT wire, to the amount flowing back to the source through the NEUTRAL wire. They are supposed to be exactly equal. If they are not, the GFI concludes that some electricity is escaping somewhere - it doesn't know or care where. It assumes the leak is dangerous, so it cuts off the power. A GFI will do this whether there is a ground present or not.
If you have a generator, and the generator has, or does not have, a neutral-to-ground connection, the GFI still looks at the balance between hot and neutral. And if there is an imbalance, it will still cut off the power. Again, it doesn't know or care where the leakage is.
I won't delve more deeply into the issue. Instead, I will refer you to an accepted RV electrical expert named Mike Sokol, who deals with this question every month, it seems. Rather than going all theoretical (as I tend to do), he simply recommends making a neutral-to-ground bonding plug for about a buck. You plug it into your generator, and it connects (bonds) the generator's neutral wire to the generator's ground. Now your generator is ready for either RV use, or usage for household standby power. As Mike notes, the lack of a ground connection can upset a so-called "smart" surge protector, and a bonding plug fixes this. But it has no effect on a GFI.
Check out Mike's explanation here.
http://noshockzone.org/generator-gro...utral-bonding/
Bill