If the NFL suspends a player who isn't charged with an offence or against whom charges are dropped, I suspect they could find themselves in a sticky legal situation.
Possibly, but an employer doesn't have to abide by the same burden of proof (proof beyond a reasonable doubt) in order to discipline an employee. Similarly, the employer does not have to follow and abide by the Court process in weighing and handing out its own discipline.
There will be times when there is a domestic dispute called in by the neighbors and there is no concrete proof of any hitting, choking, or pushing. It would be hard to discipline the guy because you just don't know what happened.
Take a situation like Ray Rice's though, and you have clear proof on video that he knocked his g/f out. I think the NFL would be well within the policy if they suspended him for at least 6 games regardless of what happened in court.