Just do it, although CIC say they don't need it at the time you submit the application, eventually you might be requested and this will delay the application process a lil bit.Hi , i am in similar position .
My spouse and I on work Visa , and my two kids on Student Visa .
I saw they ask you to do the RCMP criminal check , i am submitting my application on May 10th. i saw they don't need police check if you live in canada however this say different.
I did my RCMP already , i think i should let my husband get his completed and upload it one time.