According to Rule 3 Section 4 of the 2007 NSA Rule book the answer is emphatically ... NO. I've copied that section below so you can read for yourself. Emphasis was theirs, not mine:
Sec. 4 All players, coaches, and participants must wear shoes. Sandals are considered proper shoes for non-players. A shoe shall be made with either canvas or leather uppers or similar materials. The sole may be either smooth or have soft or hard rubber or polyurethane cleats. Metal cleats or any type of shoe that has exposed metal on the sole other than a rivet may not be worn in any division of youth play. Metal cleats may be worn in all divisions of adult FP play. *PENALTY: IF IT IS DISCOVERED DURING THE GAME THAT AN OFFENSIVE PLAYER IS WEARING METAL CLEATS AN OUT WILL BE CALLED AND THE PLAYER WILL BE EJECTED. A DEFENSIVE PLAYER WHO IS WEARING METAL CLEATS WILL BE EJECTED. Any baserunner(s) must return to the last base occupied at the time of the pitch.