You cannot get 110VAC from a 12VDC battery except thru a dc-ac converter aka "inverter".
I suggest the inverter's 110VAC output be isolated from its 12VDC input. (Some inverters had/have either side of its AC output connected to the DC input - this can be hazardous.) The AC earth should be tied to DC ground for general use.
Many inverters are "modified" or "step" sinewave. These are based on a simple (3-step) square-wave output and are NOT a true sinewave as from mains/wall AC and generators.
This can cause extra heating and hence earlier failure in some loads.
It can also cause other problems in loads - eg, peak & rms voltages are not the same as sinewave; noise caused by squarish waves; etc.
Inverters like the one you linked to are commonplace in department and electrical stores, autoaccessory places and even some petrol stations downunder here in Oz.
If efficiency is critical, get a dc powered display instead.
If getting a more expensive "true sinewave" inverter, I'd suggest a dc display instead.