If I win my administrative review hearing, will this mean that my criminal case will be dropped?

No.  There are two (2) separate parts of a DUI case.  The first part is conducted and overseen by the Department of Highway Safety and Motor Vehicles and relates only to the suspension of your driving privileges.  The second part is prosecuted by the State Attorney’s Office in either County or Circuit court.  The outcome in one arena has no bearing on the other.