Sure, you can run an inverter to power 120v items.
BUT - remember that they are gonna' draw a lot more amperage at 12v
than 120v - more than 10x, given inverter inefficiencies. So a small 240 watt appliance that only draws 2 amps at 120v will draw something on the order of 25 amps at 12v
... your battery won't last long at that rate of discharge. Plus, even at this rate of draw, you need pretty hefty wiring to prevent overheating of the battery connection wires.
I've got a 260 watt solar system and three Lifeline batteries: I also have two SMALL inverters for running very small items such as an extra fan for cooling, or a cell phone charger, etc. Everything in my trailer runs off of 12v except for the microwave and the a/c.