Can an Acceptable Medical Source (AMS) sign the Medical Summary Report if the client's main disabilities are mental but the AMS has mainly treated them for physical conditions?

Yes. By signing the MSR, the AMS is only indicating that they believe the included information to be true. It is likely that the provider has spoken with the individual about his/her mental illness, seen some records to that effect, and/or has witnessed some symptoms. In order to treat a patient properly for physical health conditions, the provider would need to be aware of medications and mental health treatment.  If the doctor does not want to sign off on anything that does not pertain to their specific field of practice, they could sign a reduced MSR that does not include reference to the other treating sources, but does include reference to all of the conditions that the doctor feels comfortable attesting to.