Hypothetically speaking, yes, Nate Robinson can make the switch from basketball to football at 31. Other world class atheletes have done it, including Brock Lesner and Michael Jordan. Furthermore, Robinson actually played football in college, at the University of Washington. As someone familiar with the sport, who has played it at a near-professional level already, yes I think Nate Robinson can do it.
Nate Robinson has already made it clear that he can play basketball. If many sportsmen can find ease and talent in performing multiple sports, I say let them have a shot. There should be no limitations except for the absence of talent when it comes to letting people perform in the NFL. If he has the talent, let him try. The worst that can happen is that it wasn't meant to be and he stops playing.
Nate Robinson has announced that he plans to retire from basketball and play football. He is not the first athlete to try this - Michael Jordan famously tried and failed to transition from basketball to baseball. Although an athlete is successful in one sport, that does not mean he has the skill set necessary to succeed at all sports.
Nate Robinson's pending tryouts in the NFL are not going to go well. The last player to switch from the NBA to the NFL was 75 years ago, so history is not on his side. Robinson is also 31, an advanced age for football. This is particularly true if you are trying to learn to play a new sport at the professional level.