Nursing schools, BONs and employers
all review criminal history on a case-by-case basis.
However, schools, BONs and employers can be as finicky as they like, and just because you got through one hurdle with no problem (e.g., you get your nursing license) doesn't mean you won't have a problem with another (e.g., some facility has a "no applicants with check fraud convictions policy"). If you get into school, you still have to face the BON; if the BON licenses you, you still have to present your criminal history to each and every employer that you wish to work for.
Lots of people with criminal records have gone on to become employed nurses, so it's not entirely hopeless for you--you still have a chance. When you apply to nursing school, list the conviction and provide all required documentation, as well as anything that might help your case, such as a statement about how you have learned from this mistake, character references, etc. After that, all you can do is cross your fingers and hope for the best.
If you have questions about the legal issues or exactly what you should put down on your application, get those answered by your lawyer. And definitely have a lawyer ready when dealing with the BON.
Best of luck getting it sorted out, and best of luck with your application.