It doesn't change anything. The authograph won't add any value that's for sure. You know you can't sell a guitar more than what you paid for it (if you bought it new of course)?
I'm not sure anyone would agree to pay more than what a new guitar is worth on a used product just because the man signed it (and/or played it).
IMO it would go for the usual market price of Alexi 600, so only taking into consideration the condition of the instrument and other stuff such as mic changes etc.
For example, I sold last year (or two years ago) an ESP CS signed by Alexi for 1550. See how the signature didn't add any value? We're talking about a CS model there!
(Oh god I regret selling that guitar so baaaaaaad
)