Leaving aside the question of whether or not it could, what would happen if Little Boy did accidentally detonate?
The figures for an airburst Little Boy bomb are:
Fireball Radius: 0.06 mi
Air Blast Radius: 1.15 mi
Thermal Burns Radius: 1.33 mi
Since the most likely detonation scenario is a surface burst in a crash, the actual figures will be significantly less, but I don't know off the top of my head how to calculate that. Eyeballing a map I found on Google, it looks like one mile would take out about half the base from direct effects, plus crater at least one runway. Given the fuel and explosives about, I would guess the whole place would burn.
Using an idealized dose rate contour from Effects of Nuclear Weapons and scaling it to 16 kT, an ellipse approximately 1.6 miles long and 0.5 miles wide would be exposed to about 100 rads total dose of radiation over an 18 hour period after burst from delayed radiation. 100 rads is the point you start seeing acute radiation sickness in some people, although relatively few. In practice you won't get a nice idealized shape like that, but it should work for a ballpark of the effected area.
So, basically, North Field is destroyed. How long it takes for the radiation to die down enough to be usable depends on the standards they use. I don't know what they'd use, but IIRC their public evacuation threshold for the Trinity test was getting close to the level that would cause acute effects, i.e. crazy high even by 50s standards. I would guess a week or two, assuming they actively remediate the site, before they can start repairs.