Yes of course, braces (brackets) can be placed on teeth which have had crowns placed over them. There are special methods to ensure the bracket bonds to the crown, and braces treatment can proceed as with all other teeth.
Unfortunately, there are some considerations when placing braces on crowns. The bracket on the crown will have a higher risk of breaking off compared to a bracket on a natural tooth.
Also, upon removal, the glaze or shiny outer layer on the crown will be removed when the bracket is removed. We can always polish the crown but it will not be as shiny and smooth as the original condition of the crown. This would more of an issue for front teeth, perhaps not so much for premolar teeth which are at the side.
If your orthodontist decides that you need to remove teeth in order to create space to align your teeth, removing the crowned tooth may be a good idea, versus a good intact tooth.
Reason being, any tooth with a crown would have had quite a bit of tooth structure removed and shaved down in order to make the crown, and if root canal has not been done yet for that tooth, there is always a risk that it may require a root canal in the future. I would say any tooth with a crown would be considered compromised compared to an intact tooth. Your orthodontist will be able to advise you on this.
Hope this helps.
Dr Geraldine Lee