Jets coaches are "toying" with the idea of using Geno Smith in such a role, according to ESPNNewYork.com.
That is, of course, as long as Smith doesn't win the starting job over Mark Sanchez.
There's a lot of theoreticals here, most notably that Smith won't be able to earn the job as the team's Week 1 starter. If that's the case, then I do see the Jets using Smith's athleticism to their advantage.
While Niners QB Colin Kaepernick surge last season started against the Jets (1 pass attempt, 5 rushes, 50 rushing yards & 1 TD), Rex Ryan has liked the idea of subbing out his quarterback long before Kaepernick was streaking down the sidelines against the Jets. Under Rex Ryan dating back to 2009, the Jets used Brad Smith to similar effect and last year Ryan admitted that the loss of Smith to the New York offense was a factor. Tim Tebow was supposed to take on that role, but the team mismanaged his use by handcuffing him from throwing the ball. Also, at the end of last season, the Jets used Jeremy Kerley in a Wildcat type role.
While Sparano's handling of the offense was an utter flop, the Jets now have the QB coach who was responsible for the actual success of the Wildcat in David Lee, so it's not outside the realm of possibility that the Jets might use Smith in such a manner. In the larger framework, should Smith not win the job outright my expectation is that it would be a "warming up" period for Smith as the Jets prepare to hand over the offense to Smith should the team founder under Sanchez.