So when Spock was applying for Captain of the Enterprise after TMP in his interview when they asked him about his command experience he could only say I've only ever been in command twice in my 20 odd years in Starfleet. And they ended in disaster.Yeah, it seems like it. Sitting in someone else's chair while he's ashore is not "your" command. It's his command, and you're keeping it warm for him.
But the Galileo being off on its own and out of contact, is unambiguously Spock's command, because the shuttlecraft has no permanent captain that Spock is filling in for, and its small crew has been assembled specifically to report to Spock, not just obey whichever guy is momentarily the most senior.