I think TGIM was a deleted scene that they decided to make use of with the Day of Positivity was cut pretty late, judging by how well animated it was. I'm fine with it not being in the movie as long as it's a special feature on the Blu-Ray.
Maybe there will even be an extended cut on the Blu-Ray. I'd love that since it seems like there's a whole lot crammed into this hour and a half and they might have had to take a lot out since it's a kids movie. :P
The seaweed mustache was a cute nod and SpongeBob has almost no continuity anyway. That's hardly a positive thing that it was cut, considering that song was so awesome.
As far as it playing into the plot, it wouldn't have been any different than the first movie when SpongeBob's getting ready for work and you see him eating soap, brushing his teeth, and putting his pants on. The whole song would have set up what a positive character SpongeBob is and how much he loves his job, which is pretty important for newcomers.