Jarryd Hayne (Aussie rugby league star) had a crack at it. He did fairly well in pre-season games.
However, as a running-back, he ran too upright. Things like that get ironed out of a player's game in high-school and college football.
The NFL are not going to waste time on teaching some overseas player how to run with the ball correctly at 22+ years of age, when there's a whole host of players in college football.
The NFL obviously want to have more of a global reach by recruiting overseas players, however, those would-be players are at a huge disadvantage before they've even begun.