The scenario is unclear, but the OP says it works for him on shore power, so that is clear enough. So it is all down to whether he can do it on inverter on that little battery.
It seems possible from a steady amps point of view, but the inverter will be doing its "amps creep" upwards to maintain the watts against falling voltage, so that skews the steady amps results.
We also don't have the voltage seen at the inverter from the start for however long it stays above low voltage shut off, whether that will happen right away or last the whole hour.
The OP will find out in the morning. Hope he reports how it went! :)