The Caldwell in question is not Jim, but David who is just now finishing his fifth season with the Falcons as the director of player personnel. Caldwell does have some ties to the Colts though, where he was a youngster learning as a scout for Bill Polian. When Dmitroff took over in Atlanta, Caldwell spent 2008-11 as the Falcons college scouting director, helping GM Tom Dimitroff draft well over that period with picks like Matt Ryan, Julio Jones, Sean Witherspoon and even the now surging Sam Baker. Caldwell was promoted last offseason to replace Les Snead, who left to take the top job in Saint Louis.
Caldwell would be an interesting candidate, but he's already interviewed at Jacksonville and will interview with the Chargers soon.
I like to see that the theme that's emerging so far from the Jets is that they are trying to peel off a younger candidate for the job from a more consistent and successful program. Gamble with the Niners, Ross with the Giants, Caldwell with the Falcons ... they all have that common thread between them.