I don't think so. Although they can stay in their strollers to watch street performers in Epcot and such. But just be prepared to take them in and out of their strollers a LOT - we just gave up on loading DS in sometimes because we were walking such a short ways!
I highly recommend a sling or hip carrier (I guess you would need both ), because, as mentioned, you can't bring strollers into any shows or pavilions.