Because you said "I have not been convicted," leads me to believe that you have been arrested, and or detained. Correct?
Anyway, if they have your social security number they can find out everything about you. Literally.
More than likely, they will do a basic background check to see if you have any outstanding warrants. They will also look to see if you were ever arrested. DUI and what not.
From a strict legal standpoint, arrests are basically irrelevant if you were never convicted. Tens of thousands of people are arrested every year, and not convicted. It is no big deal.
But keep in mind, this company could basically say "He's been arrested. No way are we hiring him." And it won't matter if you've never been convicted.
Feel free to PM if you need any more info.