Department of Veterans Affairs Accountability First Act of 2017 This bill authorizes the Department of Veterans Affairs (VA) to remove, demote by a reduction in grade and pay, or suspend a VA employee, including a member in a senior executive position, for reasons of performance or misconduct. The bill prescribes VA removal and employee appeals procedures. Whistle-blower protections are revised, including by prohibiting the VA from taking any such action against a person who has a pending whistle-blower complaint. This bill provides for the reduction of federal annuities of VA employees and retirees convicted of a felony that influenced their performance while employed in such position. The VA may recoup certain bonuses, awards, and reallocation expenses. The VA may directly appoint qualifying individuals to the positions of Medical Center Director and Director of Veterans Integrated Service Network. The bill revises time periods for adverse action reviews with respect to physicians, dentists, podiatrists, chiropractors, optometrists, registered nurses, physician assistants, and expanded-function dental auxiliaries.