Sure can! Paru is a drop-in replacement, so you can just replace yay with paru and the rest of the command remains the same.

Yeah and on Arch-based systems:

Backup Packages

Back up explicitly installed package list:

pacman -Qqe > ~/packages.txt

Back up explicitly installed foreign packages list (i.e. the AUR):

pacman -Qqm > ~/foreign_packages.txt

Backup the pacman config/mirrors:

cp /etc/pacman.conf ~/pacman.conf.backup
cp -r /etc/pacman.d/ ~/pacman.d.backup

Restore Packages

Restore the pacman config/mirrors:

sudo cp ~/pacman.conf.backup /etc/pacman.conf
sudo cp -r ~/pacman.d.backup/* /etc/pacman.d/

Sync the system and update packages:

sudo pacman -Syu

Reinstall packages:

sudo pacman -S --needed - < ~/packages.txt

Reinstall foreign packages:

yay -S --needed - < ~/foreign_packages.txt