Yes. I've been welding off my current 840AH 24V batteries quite a lot recently, with a Latronics 4kW inverter and no problems, with FM80 still connected. You really want the charging to continue while welding if you can.
One slight problem you might encounter is this: I have found that when the battery voltage was a bit low with my previous 8yo batteries, ie when it is cloudy and the voltage gets down to 21 or 22 during welding with ~4kW or so load and not much charging, the FM80 display becomes garbled. If you try and reset it by turning the power (from batteries) off and on again, you lose the data for that day up to that time. If you leave it until the following morning (I assume just until after midnight) and reset it, the data is not lost and appears in the log as usual.
Apparently there is a fix for this, Outback techs in the US have told me, but the OB techs in Oz dont seem to know about it last I enquired, so I have not done anything about it. Its only been a very rare occurrence anyway, and I've worked out how not to lose the data from the log.

