Will a dismissed MIP charge show up on a background check?

I am in a bit of a dilemma. I have been filling out this background information for this job offer I have received. I have been asked if I was convicted in the past "felony or otherwise". I have contacted the local courts in regards to the MIP (alcohol) I have had in the past and they said it was dismissed. My question is would it lawful if I have just said no on the application? and my second question is that would a dismissed minor charge of possession of alcohol would show up on a background check?