To tackle the answer head on... the answer is unlikely. The Chargers are, for the most part, set at Nose Tackle, with a recent big free agent signing in Brandon Mebane starting at the position. The Chargers have the veteran experience and leadership that they would be looking for in Knighton in Mebane. The Patriots cutting "Mister Roast" is a few months too late for the Chargers to sign him.
Both veteran players are of similar age, weight, height, and experience; however, Knighton has a history of having weight problems. Not to say he can't get in shape, but this could be a concern for the Chargers and perhaps a risk they would rather avoid.