Yes you can rent a short sale home. There are many conditions that below are stated. If your loan does not allow you to rent the home, that may cause the lender to deny your short sale. Look at your loan documents to see if this is allowed.
If a tenant signs a lease, they are then protected with certain provisions. If the home is sold to a owner occupied buyer, they have 90 days to move out regardless of the term of the lease. If an investor buys the home, the will have to assume the term of the lease. Many times, with the short sale process taking time, the tenant does stay for the term of the lease.
I would, as a property manager, have to disclose the situation to prospective tenants and tell the owner his obligations as well as the tenants. Paul is correct in that if a notice of default is filed prior to the rental agreement, then it gets in to fraud, and voiding of contracts and all kinds of messy law problems. I would consult with professionals prior to renting the home.