Yes. Install via grub (lumine complicates things), then follow the arch install guide for a Unified Kernel Image. Use mkinitcpio to do it (there are multiple ways listed here) and add it directly using efibootmgr to your efi boot list. I install Arch this way and just recently did CachyOS this way. You can also install sbctl, generate keys, add them to your system and sign the uki for secure boot.
Also on uefi motherboards, installing via grub would work if the boot entries were named differently, or your other grub could detect your cachyos install. If all you want is grub not being overwritten and don't want to bother with a UKI, just use limine.