No, you cannot
grub-install /dev/disk/by-uuid/foo. This is not saying it is impossible, one might concoct a method, but it is impractical at the least.
UUIDs (universally unique identifier) are practically unique identifiers for partitions, and not the device itself. That is partitions have a UUID, but the location of the MBR that
grub-install addresses does not have a UUID.
If you generate a UUID for the device (e.g.,
uuidgen /dev/sdb) you then encounter a device.map problem within GRUB.
grub-mkdevicemap fails to rectify the problem automagically.
grub-install /dev/disk/by-uuid/de305d54-75b4-431b-adb2-eb6b9e546013, for example, you will receive errors like
grub-install: warning: File system `ext2' doesn't support embedding.
grub-install: warning: Embedding is not possible. GRUB can only be installed in this setup by using blocklists. <blah, blah, blah>
...and so it goes.
More info can be found https://unix.stackexchange.com/questions/174206/warning-file-system-ext2-doesnt-support-embedding-but-my-system-isnt-emb
This was a fun experiment. Thanks.