In my experience, copper and copper based alloys tend to shed
coatings after a while. Everything seems fine for a while, then an
oxide film develops under the paint and ruins its adherence to the
surface. I don’t think the gesso (I’m assuming you mean regular
acrylic gesso) will be immune to this.
On the other hand, painting with oil paint on copper panels has been
practiced for centuries. Here’s a description of the process used to
prepare them: http://www.ganoksin.com/gnkurl/ep822u
I don’t know if you really want to mess with the toxic lead primer,
though, or use it in jewelry.
Have you considered using vitreous enamels instead? This is a
time-honored method of decorating copper jewelry items, and is much
more permanent than any paint.