Sure! Though not exactly in the way you describe. My inverters (a XW+ and a Conext) both have "AC in" and "AC out" connections. The "AC out" connections are hard-wired directly to the main house panel. There are two sets of "AC in" connections, one for generator support, and one for the grid. These inverters are designed as hybrids, that can act as either stand alone "off-grid" units, but also as a "grid-tie" unit. They are programable as to when electricity either feeds the grid, or charges the batteries.
The different AC inputs must always be kept separate. That's to insure that the power from different sources does not cause phasing problems. There's a toggle breaker on the power center that makes sure that AC can NOT come from the generator and the grid at the same time.
However, with the "AC in" switched to AC#2 (generator), I can run the generator to directly charge the batteries while simultaneously inverting power. I have a dedicated 240V socket mounted in the wall that is hard-wired to "AC #2 in" so the generator can feed "AC #2 in" directly. When the generator is off, the circuit is NOT hot. Separate 240V sockets are wired off the main house panel, not the inverter itself, for the 240V loads.
You can go to this link to download the Schneider installation manual. It's a large PDF, and too big to attach here. It will go into far more detail than my poor attempt.
Low Flat Rate Freight! Schneider Electric Conext XW+6848 NA Inverter/Charger, 6800W, 120/240VAC, 50/60Hz, 60A Transfer, 48VDC, Sinewave, 140A PFC Charger, With BTS, 865-6848-01, RNW865684801
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