I believe if you check your stroller with your luggage, they want it bagged. They may be able to provide you with a large plastic bag.
If you gate check it, there's no need to bag it.
I've never seen people bag their gate-checked strollers. We always gate check our stroller and haven't had a problem w/out a bag. I like being able to use the stroller up until we get on the airplane and being able to use it as soon as we arrive. Many times there are no seats available at the gate and at least your little one can sit in their stroller.
If you were gate checking an infant carrier, I'd put that in a bag just to keep it from getting dirty or wet on the seat. I've had my stroller come out a bit wet on the canopy or back of the seat b/c it was raining as it came out of the cargo area, but the seat has always been ok since it's folded.
One hint- I've seen people leave their strollers at the gate without folding it, only to see the baggage people struggling and "forcing" the stroller to fold. You should always fold your own stroller- it can get harmed otherwise! And don't leave things in the basket of your stroller.
I've read that you should never check a car seat with regular luggage. It gets thrown around and could get cracked in areas you might not see.