Having just done this recently:
Yes, while you are separated from your spouse (or common-law partner) you will have your food and board covered while on BMOQ and most likely all other courses away from your partner. Your pay will start from the first day of BMOQ, though you will be considered "hired" on the date of your signing in.
You will need a copy of your Lease and other documentation showing you live with your partner (Electricity bills, for example). To save yourself some grief try to bring (or add your partner to) bills that have both of your names and address on it. The CFRC or the wonderful clerks in St. Jean are more then able to tell you precisely what they will accept, etc. You are trying to prove that you both have lived together for a substantial period of time and are co-dependant, not just jumping into the same location for the benefits.
Additionally it is in your interest to take a look at PLD (Post Living Differential) for your home location and Separation allowance (and worth looking into if they don't do it automatically, assuming you qualify)