It makes for an interesting question. If Ryan Clark - the Steelers' union representative (Charlie Batch was on the executive committee) during the lockout in 2011 - was the head of the NFLPA at that point, would the players have agreeed to the collective bargaining agreement they did?
Interesting 1 of 3 candidates 4 NFLPA pres is former steeler Ryan Clark. Steelers were only team in '11 to vote no to CBA— daniel kaplan (@dkaplanSBJ) March 19, 2014
The Steelers are famously known as the only team to not vote in favor of it, reportedly, due to their disagreement with the amount of power the union was willing to give NFL Commissioner Roger Goodell. Clark's disagreement with the appeals "process" (Goodell rules on it, the player appeals to Goodell, Goodell rules on the appeal) was understandable, given the amount of fines he incurred in 2010-11.
Clark was not fined in 2013, and still continued to be the Steelers' player's representative. He is a free agent now, and isn't expected to re-sign with the team.
Former president Kevin Mawae served as the union president for a spell despite not having a contract with the team. Provided the player is still a part of the union, he is eligible for the position.