I absolutely think Posey is a core player. I guess it depends on what your definition of a "core" player is. I go beyond the Big Three and Rondo, I look at a "core" player as any individual player that is instrumental to our success, in our case winning a championship.
If I could, I would like to compare this situation to lets say...if Big Pappi was a free agent next off-season. We know he is getting older, and his skills are starting to diminish, his stats may be down. But would you let the ultimate team player, the one giving bearhugs, rallying the team together for a comeback, hitting the occasional moonshot(Posey's corner three). Not to mention his clutch play. You wouldn't want to let Ortiz go, granted it may be a different sport but Ortiz brings to the Sox what Tedy Bruschi brings to the Pats, and what James Posey brings to the Celtics. Its okay to be sentimental towards a player when his intangibles are "that" good.