The ATV 4 can only supply HD, not 4k, but your TV will be upscaling it to 4k - if well done this won't be as good as real 4k but can look better than pure HD on and HD-only television.
Since your TV has four times as many pixels as an HD one, it could simply turn every incoming pixel into four, then it would look just like an HD TV; many televisions do some interpolation - for example colouring the upper row of pixels to partially match the pixels above it, and so on - so as to smooth over the conversion. This can make the picture look slightly sharper.