If I tell my PS4 to output at 1080p on my 720p TV will that make it overscan or "supersample" to make everything look smoother? I thought downscaling a 1080p input to 720p would look better than a 720p input. Is this right?
"supersampling" makes little sense. It's resampling here.
What will be done in the TV is a function of your TV. Whether outputting 1080p or 720p to the TV looks better will depend on how the PS4 scales textures and images to 720p and whether that is better than the TV's input resampler. But no matter what, the image displayed will only contain 1280x720 dots of information, so the resulting image won't look better than a good 720p image no matter what.
Also note "overscan" is something else, using it to describe what is happening here will only lead to confusion.
That's not how TV's work. Unless your TV has an advanced scaler, it won't show any picture at all if it's max resolution is 720P and you set it to 1080P. You'll just get a black screen.
My Panasonic 720p TV takes 1080P signals and downscale them. The picture is very sharp and not as good looking as when i output 720p.