I'm not clear on the circumstances here, but from your description it sounds like the MP's office got involved when something negative happened. Is that right?
I believe the point is that when MP office gets involved when the processing is within normal timeframes and nothing has occurred out of the ordinary, they will just get the response from IRCC that "processing is proceeding according to schedule" (or something like that).
It is of course your right to contact MPs office if you wish and some are more active than others, etc. I believe most MPs wish to help their constituents if they can - it's only a question of whether they actually can do anything. Some parts of processing such as security checks are - reportedly - relatively immune to being pushed forward.
Now, there seems to be a certain amount of speculation here that having the MP inquiry will 'nudge' the file to at least be checked and sometimes this may help if things are stuck for administrative reasons (i.e. the file just hasn't been opened in a while). Or at least make sure it isn't stuck in a pile somewhere and forgotten. My guess is that it can't hurt, but only likely to help if it actually is stuck.
BUT: I think the question here was whether an MP inquiry can help for a december application. Personally I seriously doubt that it will help at this stage, because a december file really is early in the process.
As a more general comment on timelines, after the AOR1 and biometric and medicals, there appears often to be a gap of several months in further communications (and note it seems some files get medical requests later for some reason). It isn't necessarily an indication anything is wrong. There is some inconsistency in files getting pre-arrival, ghost updates, even AOR2 notifications, so gaps in communication are not unusual. Yes, some files get processed more quickly than average - but by definition, not all files can be quicker than average.
Again, it's your right to contact your MPs office if you wish, and if you really are convinced there is something weird going on, by all means. But if it's early in process and no signs anything more than processing is going on, MP inquiry may not provide anythign useful at all.
My timeline below. 
