I seriously doubt that running an LED TV, epically if it is a "power brick" model will fry the TV.. (Might overheat the brick a bit though).
BUT: All Audio, Video and Radio gear is on the "May not work well with an MSW inverter" list. Every last blessed bit of it.
That said the key word in that list title is "MAY".. Sometimes they do, Sometimes they don't.. But why risk it. Why not just go True Sine wave.. The "May not work" list on TSW is much much shorter.. In fact here it is:
Any device requiring more power than the inverter can deliver.
Yup, that is it. the whole list.