If you have had depression, been successfully treated, and are now OK, I don't see why not. Many of us have something like this in our personal history. You might have to go through an occy health process to be selected - as many of us do - don't forget to declare it on an application form but I still think you should be OK, it depends how long ago, and which branch of nursing you'd like to study.
Contact the admissions departmetn of your local nursing university, you can but ask them!