For outland sponsorship, MICC's interest is primarily financial. They have different income-support standards than does the Federal government, but those generally don't apply to spouse-only applications.
In the event that the prior spouse was divorced, Québec also investigates whether the sponsor is in default of child support or alimony payments. I do not believe that CIC does this for rest-of-Canada applicants.
For my application, my sponsor and I filed for our CSQ on 9 February of this year. It was issued on 19 February, and we received the letter in the mail a few days after that. MICC's official forms are of course French-only, and generic English-language translations (without personal information filled in) were provided as a "courtesy."