You can create any kind of game with Stencyl.
For your type of game, the objects to find would be actors and the places to drop them would be regions. Each object would have to have a behavior attached to allow it to be dragged by the mouse, and each scene would check for these objects in the appropriate regions before advancing to the next.
It is a fairly simple game mechanic, but I don't know if there are many pre-made behaviors which would work for you. You may need to end up creating some of your own, which isn't too difficult once you get some practice.