Veterans Visa and Protection Act of 2017 This bill requires the Department of Homeland Security (DHS) to: (1) establish a program to permit eligible deported noncitizen veterans to enter the United States as, and to permit eligible noncitizen veterans in the United States to adjust their status to that of, a noncitizen lawfully admitted for permanent residence; and (2) cancel the removal of eligible noncitizen veterans and allow them to similarly adjust their status. An "eligible" veteran is a veteran who: (1) was not ordered removed, or removed, from the United States due to a criminal conviction for a crime of violence or for a crime that endangers U.S. national security for which the noncitizen served at least five years' imprisonment; and (2) is not inadmissible to, or deportable from, the United States due to such a conviction. DHS may waive such eligibility requirements for humanitarian purposes, to assure family unity, due to exceptional service in the U.S. Armed Forces, or if such waiver otherwise is in the public interest. A noncitizen veteran or service member shall not be removed from the United States unless he or she has a criminal conviction for a crime of violence. A noncitizen who has obtained the status of a noncitizen lawfully admitted for permanent residence under this bill shall be eligible for naturalization through service in the U.S. Armed Forces, except that: (1) the grounds on which the noncitizen was ordered removed from, or rendered inadmissible to or deportable from, the United States shall be disregarded when determining whether the noncitizen is a person of good moral character; and (2) any period of absence from the United States due to the noncitizen having been removed or being inadmissible shall be disregarded when determining if the noncitizen satisfies any requirement relating to continuous residence or physical presence. A noncitizen who has obtained the status of a noncitizen lawfully admitted for permanent residence under this bill shall be eligible for all military and veterans benefits for which the individual would have been eligible if he or she had never been been removed from, or voluntarily departed, the United States. DHS shall: (1) identify cases involving service members and veterans at risk of removal from the United States, and (2) annotate all DHS immigration and naturalization records relating to any noncitizen involved and afford an opportunity to track the outcome.