Is it possible to use Grub to run an EFI binary?

Yes, and here's a short example taken from Rod Smith's great page on GRUB 2/EFI Boot Loading

To chainload another EFI boot loader, one uses GRUB2 chainloader

The following grub2 menuentry example will run an EFI bootloader

menuentry "Windows 7" {
        insmod part_gpt
        insmod chain
        set root='(hd0,gpt1)'
        chainloader /EFI/Microsoft/Boot/bootmgfw.efi
}