I have no way of knowing how Barnidge would feel about it, but he certainly could be useful as a #3/rotational TE for the Pats, as long as he can block decently enough.
Hard to know how much in demand he'd be at age 32 with so many (supposedly) very good young TEs coming into the league from this draft class. He was due to earn $3.3M + $1M roster bonus with the Browns in 2018. Hard to imagine teams offering him much more than half that.
Anyway ...
6055/243+, 4.65/40, 31" vert, 6.92 3-cone (at the 2008 Combine).
Caught 18 of 37 targets for 320 yards and 1 TD in four years with Carolina
(< 1 tgt/game).
Caught 160 of 250 targets (64%) for 1938 yards and 13 TDs in four years with the Browns (about 4 tgts/game).
Turns 32 on Sept. 22nd. Even so, he still seems like decent competition for the #3 TE spot.
... He caught 55 of 82 (67%) for 612 yards and 2 TDs in 2016.
... Bennett caught 55/73 (73%) for 701 yards and 7 TDs for the Pats in 2016.