That is very cool, but the head cracking is very EEEEEEK!

Slathering glue into the channels wont hurt, but unless you are getting it right into the crack to bind it all up, it's possibly not as effective as using thin CA glue and wicking it into the cracks.

Chances are it may settle or be a big problem, only stringing it up to tension and leaving it will tell.

There are some interesting things that you could do with dowelling etc from the edge through the cracks to try and reinforce it but you'd really want access to a drill press to be precise in placing your dowel holes. It would also then leave you with a number of little circular highlights on a very visible surface of the headstock.

I'm quite surprised that the headstock has behaved like this unless there was already a flaw in the timber itself?