Care And Readiness Enhancement for Reservists Act of 2017 or the CARE for Reservists Act of 2017 This bill authorizes the Department of Veterans Affairs (VA) to provide counseling without referral, which may include a comprehensive individual assessment, to any member of the reserve components of the Armed Forces who has a behavioral health condition or psychological trauma. Outpatient services shall also be available to such reservists. The VA shall evaluate current and future workloads to determine whether more Vet Centers, including mobile Vet Centers, are needed to handle an expansion of services resulting from such increased eligibility. If a Vet Center's workload treating members of the Armed Forces exceeds its workload treating veterans, the VA shall enter into discussions with the Department of Defense (DOD) to determine whether a reimbursable memorandum of understanding between the VA and DOD for the center's services is warranted. The VA may furnish mental health services to such reservists. Such reservists are included in the VA programs of: (1) comprehensive suicide prevention, and (2) mental health treatment for veterans who served in classified missions.