Ground on Elite 100V2

Just thinking ahead here and seeing if this is possible.

I’m considering using the 100v2 as a ups for my furnace (gas furnace, need electricity for the blower + electronics. draws approx. 200w in stage 1 and just under 600w in stage 2). AC will be out of the equation here.

I currently have the furnace wired to a plug, so during an outage i’m able to unplug the furnace and plug into my generator. Keep it safe as there is no chance to backfeed into the grid. The only problem, this furnace needs to see a proper ground, a floating ground won’t work. On the generator, I run a bonding plug and it works fine.

So on the 100v2, I’m assuming that when it’s on grid power, everything will work as the ground is connected to the house. As soon as power is lost and the unit switches over to battery, is the grounding pin still connected? or does the relay completely disconnect the system? Also, Leaving a bonding plug in the unit is a really really bad idea if it’s connected to the grid? (I’m kind of new at this and still trying to wrap my head around how this all works). What about the “grounding screw” on the unit? Manual didn’t really say what it was for. If it tie this grounding screw to the electrical box on the furnace (and hence the house ground) does that work?

My parents place has a proper transfer switch installed, and in that case, the ground goes through the transfer switch and ties back to the main panel ground, so no need for a bounding plug for them. They just plug in an go