i'd say not. i never noticed mouse lag with my tele, it seemed just like using a monitor until online fps multiplayer or twitch platformers, ppl weren't where i was aiming in online play.
other than that i found the pc+tv gaming/use experience really positive.
and yeah monitors have input lag too, the more bits and pieces the higher the input lag usually.
bits and pieces = speakers, inputs, controls, usb hubs