I would imagine that it would be very odd if they did not check.
How do you 'avoid' the whole subject of URNU. Obvious questions would be 'what did you do at . . . ?' 'Why did you leave the URNU?' etc.
They may have access to reports etc, your CO may know someone in the AIB. At OASC they often send board members to AFCO recruiting shows to see how the AFCO applies the initial filter - 'where are you from?' Persia. 'That's Iran isn't it?' Well yes but I like to think of myself as Persian. 'Sorry British nationals only, next.'
Your best bet is to put as best a spin on it as possible and tell 'em how you have learnt how to control your alcoholism and rampant instincts. If you get accepted you will then have a year or so to prove they were right.