Can an untreated broken nose be fixed without plastic surgery?

Nasal reshaping. Deformity of the nose secondary to fractures can be corrected by non-surgical means if minor/subtle and only requiring some fillers to camouflage the contour issues but the more obvious deformities will require surgical correction. See your local plastic surgeon.
Yes. Depends on how badly fractured it was and how soon after you saw the surgeon.. Within two weeks it can usually be set without the need for surgery.
Definition of fixed? Broken bones will heal on their own in the majority of cases. If there is an acquired deformity associated with the healing there are many options to try and address the deformity some surgical some non-invasive. You should see a board certified plastic surgeon or ENT doctor for an evaluation. Btw if the nose healed without intervention and there is no appreciable deformity than nothing to do.
Maybe if fresh inju. If your fracture is fresh and just a few hours old you can possibly reduce it or manipulate it back in place with finger pressure with out surgery. Similar to some dislocated fingers. If the nasal trauma is old and the bone has already healed then surgery is needed.
Yes its possible. It is possible if the nose is broken and reduced realigned quickly just after the fracture. This can be done without surgery. That requires a surgeon to promptly reduce the fracture within hour of its break .
Broken noses. That go on to heal require surgery to repair it to its preinjury appearance. You can fill dents with filler but bony deformities require surgery.