That would be a foolish and unneeded risk. Dickey's value is not going to be any higher than it is now, and you risk him have a bad 1st half, and/or getting injured.
It would be foolish for the Mets to go into the season with him unsigned, knowing that he won't negotiate during the season. Plus, other teams are aware that Dickey won't negotiate in-season, so they know they'd have the Mets at a serve disadvantage in July.
Plus, the new rules in MLB don't allow for steam get draft compensation if they trade for a guy in July, and he ends up walking on them after the season. They only get draft compensation rights if they trade for him in the off-season. Thus, Dickey's value takes a hit in July.
His situation MUST be, and will be, resolved this Winter, not in July. He's coming off a CY young season, and his stock is at it's apex now.