No, they don't. If they don't like you or feel like you can wait longer, then it never gets to the MP. Unless, you play golf with your MP or run into him at the parking lot, all comms go through their staff
Well, there's a lot more to it than that - but yes, surprise, public figures have staff to manage their time, reputations, use of resources, etc. This is true in the public and private sectors alike.
And for anyone who hasn't figured this out: one of the first and most important rules of this is to play gatekeeper, and keep the crazy, dangerous, deranged, unrealistic, etc., away from the principal.
Does this mean they have to 'like' you? Not exactly - but if the reasons they don't like you coincide with a perception of any risk of having something to do with you, yep, being not-liked is going to harm you. (General rule of life here: being liked by other people is often a big help - not always but often). It's worth keeping in mind - the staff that get results from IRCC and/or their own MPs are probably the ones that know when to be polite and nice, and value that behaviour in others.
That said: both MPs and staff vary in what they care about, but the MP sets the tone. Not all MPs are interested in immigration issues, and not all are very interested in helping their constituents. Most care somewhat, though - helping your constituents may not win you a lot of elections but not helping does lose some, word of mouth matters.
After that luck of the draw stuff though: staff and MPs are busy. They're going to treat routine inquiries ("hey what's up with my app") as routine and do no more than the basics. And they're probably going to treat 99% of first inquiries as routine, and only expend additional work on the ones that come back after the first inquiry (after a respectable period, i.e. 'avoid spammers.')
So make their job easy: write concise, simple, clear explanations of what the problem is, and why it deserves their attention, and what exactly you are asking for. Don't write novels - write short memos. If you need to include anything voluminous (like evidence), include ti as an attachment. Appear credible - don't ask for impossible stuff. Don't write screeds about how everyone in IRCC is against you or make broad claims of racism, discrimination, mistreatment, etc unless you REALLY have proof. (In fact, most longwinded complaints are going into the 'circular file' that every office has for correspodnence with crazy people).