A CVT probably could be used with a TV as long as it is an analog type producing a sinusoidal wave form.
A digital inverter producing a PWM output that is not shaped might be detrimental to the TV’s power supply.
It would be a good idea to consult the manufacturer before using any of these devises for their recommendations especially if it is a new Set with warranty, as misusing the product could potentially void the warranty.
However, the fact that you are talking about an LED TV makes me think that your TV is most likely NOT an analog set. However, my recommendation to check with the manufacturer just in case still stands.