I know that they don't except kijiji so I wouldn't think Craigslist would be excepted on its own. If the ad was placed in places like indeed, monster or other national job site places as well I'm sure it will be ok.
I know my company has placed in Job bank, indeed, wow jobs and kijij I think as well as local papers. They also placed an add for 1 month on indeed before even placing the ad on Job Bank.
You have to make sure they prove they have done all they can to hire a Canadian or PR first. Placing on Job bank and Craigslist I think will not be considered as doing enough. I've heard of others being rejected for this and they have had more ads placed.
Hope this helps. Can I ask what your job is?