If you go to court and say, "You did not properly abstract my suspension to the DMV, and they say I have a valid driver's license", then the odds are they're going to abstract the suspension and suspend your license. If, on the other hand, you drive while on probation for your DUI, even with a valid license, doing so may violate your probation per the suspension that is part of your criminal sentence. Also, weird and wacky things can happen if the judicial suspension is abstracted to the DMV down the road - as in, the DMV might start your suspension at that time.

Unless your goal is to have the three year suspension put into effect, sort of a "taking your lumps" outcome, I would find a lawyer in your state who is very familiar with DUI-related suspensions and driver's license appeals and decide on a next step after the consultation.