Can a UV LED cause air ionization? I am thinking of the high power LEDs at around 250nm wavelength and an output power of some 30mW optical, in continuous mode either divergent beam or focused.
 A: Let's look at the primary constituent of air, nitrogen. The ionization energy of nitrogen is approximately $1400~\text{kJ/mol}$. This works out to be approximately $2.25\times10^{-18}~\text{J/atom}$. 
The energy content of a laser beam is $E = h c /\lambda$. This means we can solve for a wavelength, $\lambda$ that provides enough energy to ionize a single atom of nitrogen. 
This wavelength works out to be roughly $88~\text{nm}$. 
So no, it would appear that $250~\text{nm}$ is not high enough energy to ionize the components of air. 

While I certainly appreciate the upvotes (and maybe they are a sign this is an okay way to approach the problem), the are some questions raised in the comments about some discrepancies with other approaches. So before upvoting, please read the comments and see if there is a way to reconcile things. 
And if this is okay and you still want to upvote, then please do so but help out and leave a comment saying there is no problem!
A: well. There is a paper that can clearly answer your question what you can expect  since it is the same wavelength.
http://aip.scitation.org/doi/figure/10.1063/1.3692090
Figure #4 gives that from small intensities < 10^9W/cm^2 you'll have linear ionization of organic atmospheric impurities (250 nm= 5ev quanta energy which is capable to provide direct photoelectric effect from most materials except Platinum). Though the actual yield will be low (<10^12 electrons/cm^-3) it will actually be air ionization. 
