Yes, hospitals can perform Level II evaluations -- provided they have the qualified staff. In order to complete these evaluations, hospitals would first have to negotiate payment rates with the relevant state agency.
The risk of allowing hospitals to perform Level II evaluations is that they may wish to make beds available for new patients, and therefore may be more likely to determine that an nursing facility care is appropriate. To avoid creating improper incentives, states should not delegate the determination function to hospitals. Rather, that function should remain with the state mental health authority or state intellectual disability authority.