If it really should be a crack in the actual wood, just pour (ok, wick) some superglue in there and it will be "as good as new".
Since the crack doesn't go all the way down to where the truss rod is, i'd say there is litle chance of the guitar being a lost cause, even if it had sustained a nasty hit to the headstock.
And to put my position on this into perspective, i own three guitars with glue in the headstock/neck area - they sound just fine, and are as solid as any other guitar of that model.
even if the crack did originate in the wood, it would have no impact on the structural integrity of the headstock running along the axis like that... but there's a pretty low chance that the crack would be any longer than length of the crack visible in the surface..
It's just Poly doing its thing... down side, it is might flake off, but, hey.. we like 'em reliced don't we?''
I own two Cort guitars. Both have that LP body shape, but without the contour top. I paid $100 for the first one, $200 for the second. Neither had a crack. They are not my favorite cheapies, but both play nice, stay in tune. The solder work inside was messy as hell in both of them.
If I was buying for myself I wouldn't have issue with the crack, but depends on the definition of cheap and what else was available at that price.
I would never buy something with a crack or defect for another person. Gifts shouldn't have defects.
I don't buy instruments for other people. If someone is at my house and are playing one of my cheaper guitars I might say, "if you like it is yours, take it home." I would never give them a guitar they haven't played first.
I'm on the hunt for a cheapie for a friend - got a line a Cort for silly cheap but can't play it first. Seller is clueless - what do we think? Finish crack or something more sinister?
Not worth your time.