We had a young woman come through rush one year, who was temporarily confined to a wheelchair. Panhel bent the rules to allow her mother to wheel her around during rush. (She hadn't had much practice handling the wheelchair herself.)
She did join AEPhi.
We don't have a house, so that wasn't an issue. As for activities, she just didn't let herself be limited.
She could move around for brief periods without the chair, and it wasn't too long before she didn't need it any more.