It all depends. Did you actually use marijuana? If so, and you are honest on your PHQ, then I'd still say more than likely you won't gain access. Also, it isn't the first time anyone in access has seen a case pleaded down from what it originally was so they certainly know how the court system works with those charges. Even though you plead it down, your original charge is what they will see when running your background. In this case, it is a drug/alcohol related offense within the past 5 years. The FAQ's and many other posts I have been a part of explain what that process entails. But the most important thing you will need outside of the plant is a substance abuse evaluation.
Right now my suggestion is to just take care of the court situation. Once that is done then you can worry about the other stuff. As of right now I don't see why anyone would risk giving you access.
Wish you the best, hope you turn it around.