Just be prepared that it will come up on the background check. And the battle will not only be acceptance into a nursing program, but then acceptance into a clinical site. Many people do go on to graduate with a record, but may find an issue getting clearance to sit for the NCLEX or approval from the state BON to be licensed. Even records that have been expunged will still show up on the background that state boards will run before granting you a license (some people think expunged means state boards will never see it - they will).
I would speak with the school, and also speak with your state's BON, and see what they have to say. Each state is different in how they handle students with a record. Also, each clinical site is different as well. In the program I was in previously, one of the people in my class was denied clearance to enter into clinicals because of a theft charge on her record from nearly 10 years before. The clinical site denied her, and she was forced to leave the program. But a friend of mine, attending a different school, was allowed into her program and into clinical sites with a disturbing the peace charge from about 6 years ago. She hasn't graduated yet, she's set to graduate this year, and I'm not sure if it'll affect her sitting for NCLEX or not.
You may want to check out the nursing with a criminal history forum here on AN: Nursing Licensure With A Criminal History
I commend you for changing your life around and looking to do something positive. I hope they allow you into the program so that you can pursue your future. Good luck!