Oops, my bad. I said watt hours when I meant amp hours, and was too quick with the failed arithmetic for which I apologize. Maybe the second cup of coffee will help.
Let me try again. With your LiPo battery, as I recall, you can actually use maybe 70-80% of total capacity with each charge cycle, unlike other battery technologies which typically assume ~50%. So, that leaves about, say, 80 amp hours of useable capacity. If one assumes that your cob is 120 volts, you also have to account for inverter efficiency which I doubt would be much more than 90 or so percent, which would leave you with ~72 amp hours, or 72*12volts=864 watt hours. So, on a full charge your cob could be run for ~14 hours.
So, you are correct, it might be feasible to grow a plant on battery power, and it would certainly be feasible to reduce the power bill if you already had the solar panels, charge controller, batteries, and inverter sitting there anyway. A second LiPo battery might cover all the other stuff like fans and so on, and would give some extra capacity for poorer charging days. And of course, you would need backup options for cloudy weather when solar could not keep up.
Go for it mate, you would be the first here to do a battery supported grow! Sorry about the earlier brain fart. Early morning, grey hair and not enough coffee.