Will a marijuana possession arrest come up in a background check for an internship?

I was charged with marijuana possession and narcotic paraphernalia in December 2014. I am a current college student and I applied for an internship. They went through 170 applications, had 40 interview, asked 6 for a second interview and I was one of that six. At the interview the lady basically told me that I have the job, but final offers are Monday (tomorrow). I needed to do a background check and I am under the HYTA act. The narcotic paraphernalia charge was dropped. I was told this is not on my criminal record and will stay off if I complete the one year of non-reporting probation. However I am nervous about the arrest records. What type of information will they have access to and how is this normally handled? This is a huge opportunity for me and I want to know what to do if they confront me about it. I said I've never been convicted of anything because my record is clean (to my knowledge). It's for a marketing/communications internship.