Ortiz wanted certainty beyond this year, that's why he was so fixated on getting it done now or (at the latest) by the AS break. If that situation you described were to unfold, I could see Ortiz feeling "disrespected" (millionaire problems, never will understand them...), rejecting the offer and then signing with the Yankees out of spite (the only team I could realistically see throwing caution to the wind as far as signing Q.O. players at that age, as demonstrated with Beltran) or, worst case scenario he waits until after the draft and signs with the highest bidder. Either way, the Sox would not only look bad, but would get hosed either through no draft compensation or having to see the face of their franchise 19 times during the regular season.
In any event, it's a moot point though. Papi got his security, Sox brass looks good, and everyone is happy. Now all that's left is to see what those shiny new WS rings look like!