usually an MP can inquiry abt ur process for u; many embassies don't answer to emails or calls from the applicants, but they SHOULD answer to the MP which asks on ur behalf and also they SHOULD answer much faster
however they cannot speed any application and many will refuse to do an inquiry if the file didn't pass the average processing time (or they say they inquiry but they actually don't)
also their inquiry has to b very specific: if u just ask when i'll get the visa, how long it still takes, probably they don't have any definate answer; but if u inquiry abt things like: did the embassy receive my updated mailing address, passport documents, medicals then they might b able to confirm that with u; later in the process they will also b able to say if the background checks r done, or security checks, if the interview is waived, etc
some ppl argue and cic also states that in the guides that inquiring before the average processing times might actually delay the process; noone can say if it's true or not: maybe when u inquiry they will take out the file from a queue and u loose the turn; just something to keep in mind