You will have to park your stroller outside of the attraction line. You will likely see many other strollers. Don't leave super-valuables on the stroller, and you may want to put something on your stroller to decorate it (ribbon, bandana, etc.) to easily i.d. it once you get off the ride.
If you don't see your stroller where you left it, don't panic. Cast members often move the strollers around to get them out of the way. Many attractions have a "stroller parking area", but if it overflows, CMs will stash strollers out of the way near the attraction.
We have never had anything stolen from our stroller, but it does happen.
I believe that if you have a Disney rental stroller and it goes missing while you are on a ride, you can get a replacement if you show your receipt. Can anyone confirm this?
Have a great trip!