I've considered buying
one of these - I already have the lawn mower, hedger and whipper snipper, so the battery and charger are already here. Lawn mower is the older brushed-motor type but when the ground is soft and my Honda HRX217 wants to play submarine, the Ryobi just goes to work. Generally get to do my whole front yard (22m x 13m minus a concrete path and a driveway) on a single charge.
As for the Ryobi chainsaw, they've now added a chain brake (didn't have one originally) and the brushless motor is a big step up. You'll notice that the
One+ 18V chainsaw does NOT have a chain brake so it's something I'd steer clear of. The chain in the 18V version is also less capable, with only half the cutting teeth of the 36V version and a shorter (250mm - 10in) bar compared to the 36V (350mm - 14in).
An inverter would easily provide power for the chargers. Even if they had a 1 hour charger, the 36V 5Ah battery is just 180W, allow 50% for overheads = 270W and still not much to worry about.
Where you'd get into trouble with an inverter in a portable solution is trying to power
one of these. Yes it's got a 400mm bar and it's technically around 3hp, but providing 2300W of 240V AC via an inverter has other issues - like current draw from the battery being up near 200A - you could start a 4cyl car with that power draw, don't use a deep cycle for it! Even your common generators (Honda Eu20) can't supply the power needed.
So for small operations (recovery, opportunistic grabs at firewood etc) a cordless job is ideal. 18V probably not, despite its cheaper price (and the fact that I have half a dozen 18V batteries and 3 chargers) because you'd want to cut wood, not rub it to death. Stihl make a good unit but its power isn't far in excess of the Ryobi 36V brushless unit so if you already had some Ryobi gear, going Stihl wouldn't make sense, but if you were just starting out - Stihl make a good range of cordless gear.
You can't really charge the thing via an inverter in the cabin. It's not that the batteries give off gas, but your cig lighter is rated to 10A, and 270W (the guesstimate from above) is about 22.5A so you'd do a fuse in rather quickly. The highest charge rate (allowing an amp for losses) is about 80W in the cabin. If your charger does that, then you should be fine, otherwise it's in the tub with some heavy cabling!