It’s possible. I think they would have to do a retelling of the Mitchell story, and not a continuation of it. So, I’m not sure where the vengeance angle comes in. If it were Mitchell wanting vengeance against Kirk for leaving him for dead on a hostile world (that plot sounds kinda familiar), then I could see it. But... then they would have to rehash the backstory for the benefit of the audience, which I don’t think they would want to do.
Plus, this is a young Kirk who probably hasn’t been commanding the ship for very long, so I doubt he has had time for his old adventures to come back to haunt him. So, if it was Mitchell back for revenge, they wouldn’t have the personal angle to work with, and it wouldn’t be as powerful emotionally.
The trailers suggest that Mitchell, if it is Mitchell, is out to get revenge against the Federation, not Kirk.