By altering the the current procedure, and having the students take the field, this could give the appearance that the athletics department and ultimately the university is taking a stance on the matter. However, I would imagine that there is a policy somewhere stating that the university as an organization is not allowed to take a political stance on any issue. I fully support what the NFL players are doing, but I think it would be unwise for the coaches, athletic director, and the university itself to do this.
I think on a lower level, this would only stand to alienate some teammates. Much like I do not agree with having the team pray before a game. Some students may have other ideals and thoughts about the whole issue and may feel pressured to do something they may not want to do, or risk being ostracized. We need to remember that most of these guys/gals are still pretty young and trying to figure out what it is they stand for and who they truly are.
NFL: go nuts!
College athletics: not on the field