The trade will happen. AdGon can't stop it. He doesn't have a no-trade.
What might happen is the Red Sox will delay the extension until April 5th--for two reasons; 1) to see how his shoulder is, and 2) to wait until Drew and Ortiz' salaries are off the books (April 5th). That puts them well below the luxury tax, and allows them to spend more money this year, since AdGon only adds $6 mil this year. Speier, of WEEI, has spelled this all out.
Actually, the more important reason might be the second one for the Red Sox. I'm sure they knew what they wanted to do before they made the trade. AdGon really can't do anything about the timing to negotiate the extension. Sure, he wants it now, because of his shoulder. But he can't really control it, the way I see it.
Actually, I'm surprised they opened an extension window. Maybe they are serious about extending him now. Or wanted to discuss parameters of an extension, to be finalized later. To make sure they are on the same page. Either way, I doubt it affects the trade. It looks like a good deal for Boston.
One other thought: the Sox opened the extension window now because they thought they might have some leverage with AdGon's shoulder. Extending April 5th might result in a bigger contract. There are win-wins on both sides here.