Got job offer at Geico...Will they still hire me after seeing I have battery misdemeanors?

I have 4 battery misdemeanors from a few years ago...(abusive boyfriend....I never hit anyone...arrested both of us).....but all the charges were dropped, so I never actually spent jail time for any of them, excep the very first which ended in me getting probation for 8 months. Will they still hire me? I am scheduled to start training next week!