Seems like yes if you side load f droid https://www.reddit.com/r/termux/comments/d4rqma/termux_on_a_...

You don't need to root the FireTV stick at all. You can install termux from the F-Droid application by installing F-Droid first by installing the APK from the Downloader app.

If you want to root the device for fun, I wrote a little tutorial post a few months ago https://miguelmota.com/blog/rooting-a-fire-tv-stick-4k/

You might want to check out adbLink[1]. It makes managing firesticks pretty simple.

1: http://jocala.com/