Upon further thought, I think yes,this could work. However I still don't think it's the way to go.
You can charge it easily enough, it's only a 6S unit. Off the shelf battery management charger with balancing capability would work. The efficiency will be low, since you are charging one battery pack from another, each with inefficiencies. plus inefficiency of the inverter. Cooling may be an issue. I didn't see on the inverter data sheet the Voltage range for operation. You will need a protection circuit to make sure you don't over discharge the battery pack. But it could work.
I'd still suggest spending the money to install an EVSE at some place along your route. For $1K you can buy one and have it installed. Find someone who will let you use it in exchange for installing it at your expense. Easier, faster, safer. I'd try this approach first. Or, as I suggested, just a 220 outlet.
2013 FFE Returned after 3 years with 52,000 miles and battery down to 15.2 kWh
2014 Volt returned with 43,000 miles
2014 Volt 26,000 miles
1967 Corvette 427
1962 Corvette 327
Awaiting a Bolt