Is it possible to verify grub installation without rebooting?

I don't think you can just check whether this will works or not before trying to do it, but instead you can get a preview of your GRUB instantly so you can be sure that your new configuration is loaded correctly in GRUB.

This could be achieved using a tool called grub-emu.

man grub-emu

NAME
       grub-emu - GRUB emulator

SYNOPSIS
       grub-emu [OPTION]...

DESCRIPTION
       GRUB emulator.

       -r, --root-device=DEV
              use DEV as the root device [default=guessed]

       -m, --device-map=FILE
              use FILE as the device map [default=/boot/grub/device.map]

       -d, --directory=DIR
              use GRUB files in the directory DIR [default=/boot/grub]

       -v, --verbose
              print verbose messages

Easily install grub-emu using command line:

sudo apt-get install grub-emu

To run it just use terminal to run this command:

grub-emu

This answer uses file -s /dev/sda to see if the GRUB MBR has been successfully installed. Past that, you could definitely double-check the values in /boot/grub/grub.cfg to make sure the UUIDs match up with the values in /dev/disk/by-uuid, and make sure that everything looks right in /boot/grub/device.map. If that file is wrong you'll have trouble with (hdX) specifications in grub.cfg.

Managing these files manually isn't necessary though if you're using update-grub after installing grub on replacement drives. The biggest gotchas in my experience have been not updating the GRUB configuration, not installing GRUB on all the drives, or improper partitioning that makes it so you can't install GRUB without using --force.