Yes, you can (I am in the same situation, but got AIP in March, the same time as CSQ request).
Already I am waiting for the first RAMQ. I had to add to RAMQ form: a CSQ copy, AIP printed and work permit copy (I applied for SOWP the same day as sponsorship and then added docs via webform, it took about 150 days to be approved). First, call them, you need to have a file and then they send you form via snail mail, you have to sign it and add docs they mention to you on phonecall and thats it! Good luck!