Is it possible to treat a compression fracture of c6 without surgery?

Possibly: Can't know for certain without more information.,if the spine is stable, a brace can hold alignment until the fracture stabilizes, sometimes 'glue' injections to the fractured vertebra may work as well. Seek guidance from a neurosurgeon who will look at MRI and X rays to best advise you,mother get a 2nd opinion from another surgeon if desired.