One time, when it was exceptionally quiet and exceptionally well staffed, we were able to keep DD in her own wheelchair for the whole line. The CM then took her wheelchair to the unload area and it was waiting for us. That was once, a long time ago and I doubt that it's more than a once in a lifetime experience. As Steve mentioned, the load and unload areas are actually in 2 different buildings, so it would require a special set of circumstances (and quite a bit of CM time) to move a wheelchair from boarding to unloading. The unload is even a floor below the load area. There is no way to load a wheelchair party at the exit and then ride on thru to the regular boarding area for Pirates (after the unload arrea, the boats go thru an area with only enough clearance above them for the boats to go thru).
If your non-folding wheelchair is not too big or too heavy, there might be an alternative. On our last trip, we explained to the "greeting" CM that DD just would not be able to ride in one of the loaner wheelchairs and she is much too big to carry. The CM looked at DD's non-folding wheelchair and said that if we could take DD out for boarding, they should be able to load it on board the boat since the wheelchair was narrow, not too long and not that heavy. The final decision would be the load CM's, so we might have to wait in line and then not be able to board. At the boarding and exit areas, we still had to deal with the metal bars that separate the areas into rows for orderly boarding. When we got to loading, the CM had us get on, he saved the row behind us and lifted the wheelchair into that seat. He said it was not that much harder than hoisting in one of the rental folding wheelchairs. The wheelchair rode with us and at the exit, the CM took it out so we could put her back in.
Another alternative that we have used in the past is to have one of us sit in the loaner wheelchair and hold DD. Then get out at boarding, have the CM fold the wheelchair and load it into the boat. That worked OK for a few years while DD was small enough to hold (sje's much too big to do that now) and we had enough people to push the wheelchair.