Provided Inverter is a true sine wave no problem.. NOTE: many TV's today are 12 to 14 volt and will work fine on auto power... Many are not.
Some considerations.. ELEMENT Tv's are the only ones made in the USA.. They do not work with most digital cable systems however
I have a Samsung that is 14 volt,, Some folks worry that a 12 volt TV will be damaged by charging voltage,,, not my Samsung..
Many Samsungs are "Smart TV's with web connections mics and cameras,,,, Just what you want (not) in the bedroom.
There are other things about other TV's. but if I list all the possible concerns I'll still be typing tomorrow.