Well. it is a modified sine wave.. This means there is a long list of things that MIGHT not like it.. But... Considering the price (Effectively $0.00) and the degree of incontinence if it does NOT work for your Tv.. I'd say go for it.
Put the inverter NEAR the batteires (Compartment next door)
Run 120 volt wire up to the TV compartment and install a 2nd outlet there, make this one either RED or ORange, plug TV (And other related stuff) in to this outlet and see how it runs.. Problems, go with a 300 watt TRUE SINE WAVE inverter.. Degree of inconvience.
Well to swap out the inverters you pull plug, unhook two wires, hook wires back up and insert plug.. So you do very little extra work.