Most headstock breaks can be repaired. There is a certain glue that I use which is a trade secret - many repairers dont know about it!
I have seen guitars that customers have tried to glue back with PVA glue - or even super glue - and this just makes it a longer job to clean out the wood grain.
I repaired a cheap 1/2 size guitar of my own in the past, the headstock had come off completely. I left it for 1 week after glueing, then purposely broke it again. It made a fresh break 2 inch's below the glued area. This shows how strong it is when done correctly.
I always refinish the area as this helps to seal the repair for a life long repair.
Some repairers route out slots to glue in wood splints. I prefer not to use extra wood as I don't feel it's necessary.
set up | string change | pick-up fitting | nut fitting | bridge/nut adjust | piezo fitting | pre amp installation