It is possible, but my guess is that it would be kinda difficult, or if you took it to a luthier to fix (probably the best route) it would be expensive. that is quite a crack you've got going there.
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It doesn't look too bad. Definitely workable.
Get some wood glue in there (Titebond, or other PVA type glue), and clamp that shut for 24 hours. Should be good to go.
This is a common break on guitars, and yours is quite clean actually.
That is definitely fixable. I would complete the crack until you have two pieces then put some titebond or other such wood glue on it and clamp it. The end result should be stronger than the original wood. You can get some cheap clamps at Harbor Freight. Could pick a couple up for less than $10.