Can you use it on battery power through the inverter?
You'll need a pretty big inverter, and even then, not for long. A small AC will draw 750-1000W continuous; lets say 750 for argument. You need about 1.5X surge capactiy to start an AC. So first, you need an inverter with a 750 watt continuous rating and 1125 watt surge capacity.
Then, once you get it the AC started, and figuring 85% efficiency on your inverter, you will draw 74A DC continuous. A standard 65A-h deep cycle Mac battery discharged to 50% will be done in less than half an hour. Even several good sized batteries totalling (say) 250 A-h will last well under 2 hours. You can cycle the AC and keep adding battery capacity to give more hours of operation, but that becomes impractical in a hurry.
Eventually you will need to recharge the batteries. A typical 50HP outboard alternator will put out around 10 amps max. So, for every continuous hour you run the AC, you have to run your outboard at full alternator output (i.e., something close to max speed) for seven and a half hours.
Your AC, batteries, alternator etcetera, will differ from these numbers but they are in the right ballpark. Bottom line, it's simply not practical to run AC off an inverter. If you really can't do without it, plan to dock at a marina where you have access to shore power, or save up for an auxiliary generator.