Unless the appliance is defective, you can not run things with an open neutral.
The Honda gen does not have a "floating" neutral. The gen has no neutral or a hot. It just has two outputs. Depending how you wire the gen to the ac receptacle, in other words, which wire goes to the short receptacle slot and which wire goes to the long receptacle slot will define "hot" and "neutral".
Edit, didn't understand what was meant by floating. The gen outputs are floating with respect to ground or chassis. That's a don't care scenario. AC requires just 2 wires to function, not three wires. It doesn't matter if neutral is bonded or not. If an appliance is operating with an open neutral then it is defective.
BFL13 wrote:
Can't you still run things from the 120 across hot and ground? If you need the neutral, how can things run off the floating neutral Honda? (but that is not the same light as the Open Neutral on the tester)