I have never seen/heard an explicit statement from Jonny or the band’s techs about whether he is using both pickups.
However, I think that he is almost certainly using both pickups.
Jonny’s bridge sound definitely has definition, but it is still quite thick (those don’t have to be opposites). His bridge tone may be brighter than would be the case if the same humbucker were used with a standard tone knob, but the Tele Plus is also equipped with a TBX Tone control – capable of boosting as well as cutting the treble. Using the both pickups along with the the TBX knob at max, the guitar’s sound is bright, defined, and rich. But that is not the only way for Jonny’s final sound to be bright and defined.
Jonny generally favors amps which are rich in the treble department (Twin Reverbs and AC30′s) for his clean sounds, and also runs his guitar through many buffered pedals (preventing him from losing high end).
Mic’ing can also have a significant effect on the clarity and EQ/emphasis of a guitar’s sound. Since we never hear Jonny’s unmic’d sound, we don’t know how his guitar sounds “in the room”. I have personally found that Tele Plus -> Shredmaster -> Eighty-Five can lack definition in the room, but have a lot of it when close mic’d.
Basically, Jonny’s final sound being brighter than might be normal for a humbucking Dually Red isn’t really sufficient reason to conclude that he is only using one of the pickups.