How do you tell if smoky quartz has been irradiated?
It can be hard to distinguish man-made smoky quartz from natural smoky quartz. Traditional methods for irradiation to convert quartz to smoky quartz tends to leave the quartz crystals looking more black than translucent smoky brown.  This is caused in part by the rapid irradiation time for man-made smoky quartz.  I am sure a more patient man made process could produce more naturally smoky quartz.

The best way to determine if smoky quartz is man-made or not is to know the location for the quartz specimen.  Arkansas, USA produces mostly clear quartz and very little natural smoky quartz.  Dark smoky quartz from Arkansas is almost certainly artificially made.  I have a specimen of dark smoky quartz which is almost black from Bear Lodge mountain, Wyoming that is definitely natural.  

Best practice, if smoky quartz specimen does not have a well known location, assume its man-made never pay alot for it.