Human Resource professionals please respond.

I have been holding a very respectable position for 7 years. 6 years ago I plead guilty to a crime that I committed a few months after I had my child. I was in an abusive relationship, and just started my above identified job. My child's father would refuse to let me drive his car some days in order to get to work which left me no way to get there. Being this was a new position I had to think quick. I saved money enough for down payment on a car, however did not have the money to get insurance which was required to drive off the lot. I then made the dumbest decision of all time which was to use a close friends account in order to get insurance. (felony conviction)At the time I was desperate and really needed to work to provide for my child as well as drive her back and forth an hour away for doctors appointments for blood work she was born with a thyroid condition. I plead guilty 6 years ago and took responsibility for my actions. My current employer is aware of this for I was picked up by the police at this place of employment. A year later I had to redo my references so that I would be cleared by DCFS. I have now held this position for a little over7 whole years. I am helping teens who have had run ins with the law rehabilitate themselves. My question is I have interviewed and have been identified as a candidate for a position similar as mine, and my question is, if they will look at how I've rehabilitated and how I've helped others to rehabilitate these passed 7 years will be recognized or am I wasting my time on trying to get into this company?  They never asked me questions about conviction so that I can explain what happened, I am more than willing to cooperate if they do ask. Also if they don't ask would it be wise for me to call them in the morning to explain my conviction. I really want this job and don't want to be misunderstood for trying to be deceitful because I'm not I am very open to explain. Thank you for your help.