Can a broken thumb/finger bone not require realignment of the bone?
Yes. You can figure that yourself if you look a bit at the types of fractures on Wikipedia, the Bone Fracture page:


  Other considerations in fracture care are displacement (fracture gap) and angulation. If angulation or displacement is large, reduction (manipulation) of the bone may be required and, in adults, frequently requires surgical care.
  
  [...]
  
  Other types of fracture are:
  
  
  Complete fracture: A fracture in which bone fragments separate completely.
  Incomplete fracture: A fracture in which the bone fragments are still partially joined. In such cases, there is a crack in the osseous tissue that does not completely traverse the width of the bone.
  [...]
  


Incomplete fractures and fractures with less or no displacement may heal correctly in some situations without needing realignment.