During my latest hiring process with UPS, it was known that I would be driving in a matter of month(s) so I think they essentially did it as though they were hiring a driver off the street from an HR point of view. At any rate, I couldn't always distinguish whether some stuff was normal new hire requirements or driver requirements. I can't recall if it was on the "annual certification" or another document but I do recall that at some point in my latest hiring process that I signed a document that stipulated that I would notify my UPS supervisor of any accidents, moving violations, etc. on the next business day or something to that effect. It was one sentence on the entire document but I noticed it when I signed the document.
I may be completely out of whack here but I wouldn't wait until the "annual certification" anyways. If you are gonna get in trouble, then putting it off may only aggravate the situation when they finally find out. I think looper804 raises an excellent point where not telling them could potentially bite you in the butt on this particular situation. I don't know how the background checks are conducted but it seems reasonable that they check the driving record of all new drivers at some point (maybe it has already been done but why run the risk).
When the state threatened to suspend my license as I was starting the 40 hour driver training (technically, I have not completed it because I still need my Buddy Ride), I let my Center Manager (he is my supervisor) know immediately and kept him informed of what was going on. My license was going to be suspended because I had not submitted proof-of-insurance to the state of Alaska after an accident last May. Evidently, I should have been given a form by the police at the scene of the accident; however, I was not given the "yellow" form so I never sent it in. The point of all that was that I might have been in more serious pickle with UPS if I had not disclosed that accident (the other driver was convicted for his involvement and was deemed liable for the accident) in the appropriate places on the hiring application. The Center Manager was like, "take care of it because you aren't worth nothing as a driver without a license" and didn't seem too concerned.
Even if they kick you out of the class, it seems that you could work inside for another year until you had 12 months if that is the issue. Hard to say if the 12 months counted from when you get hired, start training, or start driving but you are past one of the hurdles. I'm guessing that the powers that be will appreciate your honesty no matter the outcome.