VA Accountability First and Appeals Modernization Act of 2017 This bill authorizes the Department of Veterans Affairs (VA) to remove or demote a VA employee based on performance or misconduct. The VA may remove such individual from the civil service or demote the individual through a reduction in grade or annual pay rate. A demoted individual shall not be placed on administrative leave or any other category of paid leave during the appeals period and can receive pay only if he or she reports for duty. The bill: (1) establishes an expedited appeals process by the Merit Systems Protection Board, (2) amends the disability benefits appeals process, (3) prescribes restrictions on the VA's authority to remove or demote an employee, and (4) establishes whistleblower protections. The VA shall reduce the federal annuity of an individual removed from the VA Senior Executive Service (SES) who is convicted of a felony that influenced his or her performance while employed in such position. The VA may reduce the federal annuity of an individual who was convicted of such a felony and was subject to removal or transfer from the SES but who left the VA before final action was taken. The VA may recoup an award, a bonus, or relocation expenses paid to a VA employee under specified circumstances. The VA may suspend, reprimand or admonish an SES employee for misconduct or performance that does not merit removal. Appeals may be made to the Senior Executive Disciplinary Appeals Board (as provided for by this bill). The bill amends the disability benefits appeals process. The bill prohibits payment of an award or bonus to any SES employee during each of FY2017-FY2021.