Would it have been possible for Prince Albert Victor to have become Viceroy of India?
By the time he was old enough it was clear he wasn't capable of doing such a role.
The position of Viceroy of India was too important to give to someone who wasn't all that bright and struggled to do some of the basics educationally (like his father he wasn't a great reader but his father could 'read people' which was a skill Albert Victor lacked).
The Queen did appoint her son-in-law as Governor-General of Canada but he was a lot more intelligent and capable. She refused to appoint Bertie as Viceroy to Ireland. She certainly wasn't going to then appoint her grandson to a more prestigious post than one she had denied her son and heir.