+1. SAS is still a separate airline and based on my experience just now, they follow Skyteam rules for benefits and recognition and not much more.

As a point of data : I redeemed both FB miles and also bought some Y Light tickets (paid cash). In each case, a personal item and checked bag were included as part of Skyteam benefits (I am silver), but every boarding card on their appli clearly had written No Carry-On Included.

I stuck to the rules with only a rucksack, and no one was strict about it except the misinformed check-in agent at FRA, but I would not want to pull a roll-aboard carry on if the flight was full unless the fare rules specifically stated that.