Yes obviously, the GCMS notes is not going help process the application any faster - but in case if one's application has no updates for more than several months and while cic account shows no useful information, other than standard "In processing/reviewing" status - I think GCMS notes can be good option and given that recent news about application assigned to inactive agent, if GCMS notes gives any clue (not necessarily it may indicate or otherwise) of whats happening on the file. Other options are calling IRCC like hundreds of times just to get someone or like you said, thru MP.
EE/PNP-EE file indeed move quick in all over processing and thats how it is... but when we (lowlife slum-dwellers
if you say so of non-ee) folks get the PR, I think we would personally treasure that status 100 times more than the one that gets status in just few months. I know i'd take the route of getting status in few months.. and why not? but is it what it is.