In a vehicle we do normally use the chassis as return, and often there is an earth braid linking parts, the worry is the bit of body you connect to will not have a thick enough braid linking it to rest of car, but that is unlikely.
The other worry is the effect on the battery, when a lead acid battery is discharged sulphur forms, and this can harden over time, so with a starter motor the time between discharge and recharge is very small, so the battery is OK, but when there is time between discharge and charge the charging takes longer, also most car batteries are designed for high current, and can be damaged if deep cycled, some batteries can stand it better than others, the leisure battery is a hybrid not a true traction battery or car starting battery, where a 60 Ah car battery is used, it would be replaced with a 90 Ah leisure battery with items like motor caravans, but normally we use a second battery and some form of split charging.
The main thing about split charging is the second battery is disconnected from prime mover battery during starting, so you don't draw starting current from the second battery, and second when ignition switched off, you don't discharge the prime mover battery.
With modern AGM batteries they can be left in a part discharged state for longer, but they are expensive. With milk wagons we installed Ni/Fe batteries as these could charge faster, so they could suck up the milk without engine running in farm yard and it would be recharged before they got to next farm, they were also used in buses so they could have inertia lights on what at terminus. Darn expensive things.
Using an inverter once in a blue moon is not problem, but using on a regular basis is, ask any canal boat owner. They try to once a month find a mooring with shore power, as the 6 hours the engine is running when continually cruising is not enough to fully recharge batteries, and over time they get slowly more and more sulphated. Charging lead acid takes time, does not matter how big the alternator.
Using a small smart charger 3 amp is ample over night once a week will likely save the battery for getting sulphated. But lead acid battery use is not simple maths, with things like canal boats they use stage chargers and pulse chargers, so when the engine is started it charges to 14.8 volt until the current drops to under 5 amp then goes to float charge at 13.8 volt, this means the bulk of the charge if put into the battery in the first hour, so it has 5 hours to put the last 10% back into the battery. Problem with road vehicles we tend not to drive them for 6 hours, and even 6 hours and canal boats still have a problem, today they end to use solar panels as well.
I used a second battery with many vehicles, some times so I could jump start wagons, some times to supply a caravan, as I said before in other post in your situation I would look at a jump start battery pack as the simplest way to run that machine, mine has a 300 VA inverter built in with a 12 Ah AGM (VRLA) battery, and can be re-charged from car or mains.