It's a Python command line program, so yes. I use Termux (a Linux terminal emulator), and I installed yt-dlp using pip, a package manager for Python. I also have ffmpeg for command line video editing on my phone.
I have it setup such that when I click "Share" on a URL from Firefox or YouTube, and I choose Termux as the receiving app, I am presented with a menu that let's me choose if I want the video saved to a normal folder or a hidden folder (for reasons), or if I want to download just the audio and save it to an MP3. yt-dlp can download from much more than just YouTube.
The script is just a bash script with a specific name in a specific folder that Termux knows to invoke when sent a URL. You can do anything you want with such a script.
Only get Termux from F-Droid or Droid-ify. Not from the Play Store. The Play Store version is way out of date.
Like the other person said, Newpipe can also download from YouTube. It's a YouTube front-end that scrapes the public HTML website for YouTube. You can also download that from F-Droid or Droid-ify.
Oh, and another person mentioned Seal, which is a yt-dlp front-end for Android. It's pretty great! I just installed it. As usual, it's on F-Droid and Droid-ify.