As others have offered: NOT.
All links in the chain must be 4K to watch 4K. If any link steps down to a lower resolution, that becomes the quality of what you can see. As #4 shares, your TV will then up convert whatever you feed it to fill the screen, but that is invented 4K vs. actual 4K... much as it would be if you dug up an old VCR or Atari 2600 or similar at SD resolution or below and connected it to a 4K or even 8K TV. Either would scale it up to fill the screen but obviously neither would be feeding the TV actual 4K or 8K video.
Your weak link is that AppleTV. Replace it with a newer one that can handle 4K and that should get you what you apparently want. Perhaps move the existing AppleTV to some other TV only capable of HD resolution so that they are basically a matched pair.
And one more thing: don't be fooled by computer graphics or video descriptions. There are videos on Youtube with 12K and 16K prominently shown on the thumbnail and referenced in the description like this one (of
MANY)...
Playing them doesn't mean anyone is seeing 12K or 16K- that's just graphics... like watching a video of the Superbowl doesn't mean they are replaying that game right now... or a video of a past weather warning doesn't mean that weather is also in play right now. It would be easy to make a video with the words 32K or 96K written on them, but watching them on a TV that can only display 4K or 1080 or SD doesn't mean that TV is magically able to display 32K or 96K.