I was hoping to get some clarification. If I am on summary probation for misdemeanor - driving on a suspended license in the state of California will I be able to enlist in the Navy?

NO
You are tied to a court as long as your on probation.
You cannot join as long as your tied to a court.

Shockey

Just to add something to the previous answer you also can not have them drop probation to enter the military service as that constitutes coersion to enter military service which is also illegal(and can get you booted for fradulent enlistment). Finish up your probation(and any community service) on the regular time alloted then look into military service.

MA2(EXW)

If you are not required to check in with a Probation Officer or have to go to court again for any reason what so ever, then you may be eligible for enlistment.

Get your court documents together and take them to a recruiter for a legal determination.