Serve Veterans First Act of 2017 This bill requires the Inspector General of the Department of Veterans Affairs (VA), at the end of each calendar year, to determine whether any veteran attempted but was unable to schedule an appointment to receive hospital care or a medical service within the wait-time goals of the Veterans Health Administration. The bill prohibits any VA employee from using official time for any purpose related to a labor organization: (1) before the Inspector General has made such determination; or (2) if the Inspector General's most recent determination found that such an incident occurred. The Inspector General must investigate each report received of such an incident and may determine whether it occurred.