Honda generator owners - can you use a GFCI?

[ShrimpBurrito]

I'm going to get a Honda inverter generator for home backup power. The most popular model is the new 2200 watt model (the EU2200i, which replaces the old EU2000i model). It reportedly has a "floating neutral", and so my understanding of that is such that a plug-in ground fault circuit interupter (GFCI), like this one, will not provide any protection. For those with a better understanding of this than I (ahem, Bill), is that correct?

In contrast, a slightly modified version of this generator, the EB2200i, has BUILT-IN GFCI's, made possible because it does NOT have a floating neutral, and instead has its neutral bonded to the frame. This begs the question, why would they not have a neutral bonded frame on the other model? Notably, this model lacks the DC charging circuit and the ability to piggy-back another generator with parallel cables that the EU2200i. So, while they're the same price, that's the trade off.

Dave