With TRUE sine wave inverters, the list of things that may not (or will not) work properly is very short: Anything needing more power than the inverter can invert.
That's the list
With MSW's. the list is much larger, including all forms of audio, video or radio receiving gear, And TV's are all of those (Audio, Video, Radio).
The key word is "MAY" they may not work properly, May exhibit reduced performance, or.. on the other hand, they MAY work perfectly.
You do not know till you try it.
AM radio.. Is generally a bust with MSW. but who listens to AM any more?