Sorry to hear about your job loss, I have a question which would help us answer the question, are you in Canada or China as you mentioned you received the request from CIO Beijing, if you are in Canada on a job offer and LMO then why would Beijing ask for your Passport, should it not be Buffalo?
If it is the LMO based on what you had applied the PR then yes it may impact your application
I'm in Canada now. I have worked for a Canadian company since 2009. I mailed my application to CIO and I put "BEI JING" as the visa office.
For applicants with chinese passport / Hong Kong passport, can choose any one of those visa office: beijing, hong kong, or US. visa office.