Yes, that is what the grub-btrfs daemon does.
The hook reinstalls the Grub bootloader and regenerates the Grub configuration file whenever the Grub package is updated.
Your question is kind of unclear, but it should be fine to use that hook with this setup.
You must have a 4K screen or something. I have a test machine here where the menu looks like this:
Yes, that’s perfect. Either changing the resolution or changing the font size should work. Just whatever you do, don’t follow the “tip” in the green box where it suggests using Grub Customizer! 
[FAQ] Why you should NOT use grub-customizer