I work with a bank in the Chicagoland area to rent their inventory of foreclosed homes. They certainly have the right to do so but it is not a common practice. Banks are not in the business of holding real estate but it is a product of this market. This particular bank felt it was in their best interest to rent out their inventory because the homes are not selling. Renting these properties out is certainly a much better option then letting them sit vacant.
Banks and not in the business of owning property to begin with. Leasing the property they own would create a whole new set of problems for them. So I would say that it is very unlikely they would rent bank owned property.