Daystrom Institute

I'm guessing he still would have been compelled to sing...but the content of his song may have been different, as he would have had different things on his mind at the time.

Maybe a number about gaseous anomalies.

If Kolinahr works like it says on the tin (purging all emotion), it seems doubtful that the season would have the same plot. Spock probably wouldn't have been in whatever weird mood compelled him to "steal" the Enterprise and charge off to Cajitar. It's unclear how he would have been affected if he were again abruptly turned fully human, or if Chapel could have convinced the aliens to change him back, it seems especially unlikely that the two of them would have wound up in a relationship at all. So the emotional cause for his Subspace Rhapsody solo is gone.

As for the more technical side:

Uhura: I have a theory. I think since we're in a musical reality, we're actually following the rules of musicals. So, when do characters in musicals usually begin to sing? When their emotions are so heightened that words won't suffice. This musical reality wants us to sing about what's most pressing on our minds. These emotions have the power to overwhelm our capacity for rational thinking. They also have the potential to drive us apart.

If Uhura's theorizing was correct, an emotionless Spock would have probably been involved in the ensemble songs the same as always, but would by definition be incapable of experiencing "emotions [...] so heightened that words won't suffice". So it is unlikely that he would have found himself belting out a solo about anything.