If you did plead guilty, then if follows that you were convicted.....
To answer your question as to whether this should be added to or ommitted from your application, I would say keep it in. Honesty is the best policy. Some would argue that it might affect your admission chances, though most would disagree.
If you exclude the information it is likely that the law school might never know, but if they did find out, you could be kicked out. The biggest problem, however, would occur after law school when you apply to sit for the bar exam. The state bar will go over your record with fine tooth comb running a "character and fitness" test to practice law in said state. Although they would overlook your past crime, they would not overlook the fact that you lied about it on your law school application.