Neutral to PE bond is ended for a GFCI to operate.
GFCI's are designed to work with or without a ground.
In my experience, some GFCI outlets require a ground to reset, and some do not.
GFCI is allowed as a way to put 3-prong outlet in a 2-wire circuit.
It should be used for kitchen/bath/outdoors so you don't get a shock to plumbing or earth. Regardless of whether ground wire is available.
I installed Eaton GFCI, found it wouldn't reset, instructions said it checks L/N connections.
I replaced with Leviton and it did work without ground.
A GFCI will not operate if no current flows to ground.
If no ground or neutral exist in your scenario, then you won't get shocked.
If no path to earth from inverter except one, you the person, you won't get a shock and GFCI will not trip.
If there is so much as capacitance to earth, you can get a shock. People have been experiencing that with PV panel frames. The PV wires carried about 60Vrms AC. Bonding frames to inverter with a ground wire fixed that.
If your inverter on a van powers one 3-prong appliance that is lying on the ground (e.g. electric tool with metal case) and you touch Line or the case of an appliance with internal fault, you get a shock. Cheap +/-60V portable inverters, I think shock between faulty appliance and vehicle chassis (or earth if foliage touches vehicle) would be a possibility.
The GFCI won't trip unless it detects imbalance between L and N of 0.005A or more, such as through your body. Then it will trip and protect you.
GFCI won't protect you if you grab line with one hand and neutral with the other. So long as you only touch case of appliances, don't grab bare wires, you should be protected. (Unless you're as creative as me, you could wire multiple devices to make a shock hazard anyway. But that's another story ...)