Yes, the arrest will show up on a LEDS check, and unless Cali is vastly different from Oregon, the application for nursing school will ask you directly if you have ever been arrested, charged, or convicted of a misdemeanor or felony. You have been arrested AND charged, thus you have
to disclose the truth or your application will be rejected, plain and simple.
I would suggest contacting your court of record to find out what bearing, if any, the disposition of your case might have on your ability to get into school in the short term, and to obtain licensure in the long run. By the time you are through your program, it will have been several years since the crime, and you shouldn't have any trouble getting licensed as long as you make it clear that you accept full
responsibility for making a bad decision and will never repeat the offense. (IOW, don't drag your 'friend' into it; the BON doesn't care---your 'friend' isn't the one asking to be placed in a position of public trust).
Best of luck to you. A lot of us have made mistakes, especially when we were young and foolish; thank God those mistakes don't necessarily have to define us for the rest of our lives.