Typically, jade bracelets come cut as a solid bangle or as a flexible bracelet with several sections of jade held by metal end caps and joints between pieces. With your bracelet, adding the spacer is a good idea but you will have to have two spacers, not one.
Since the solid jade is not flexible, the bracelet will need to be cut on opposite sides so each half may be connected with a spacer. You will need to find someone with a fine blade diamond saw to cut the jade. These saws are motorized using a 6" or so circular blade of thin design. Steel tools simply will not do the job. You want a fine and neat cut so the ends are parallel and match nicely.
If a jeweler cannot do this, most will not have fine diamond rock saws, one suggestion is to contact a local rock and gem shop. The rock and gem shops cater to folks who like to do their own stone polishing and a diamond saw is one of the basic tools of the hobby. Ask the rock shop if they can recommend someone has a "thin kef" rock saw. People who do faceted stones or cut opal are most likely to have the diamond saw with a fine (thin) blade and may cut the bracelet for you. The rock shop may also offer this service for a minimal fee.
Spacers will take the form of "end caps" or shallow cups into which the jade is cemented. The spacers could be made with two opposing caps (shallow tubes) for joining the jade ends, with one spacer on each side of the bracelet. Any competent bench jeweler should be able to fabricate the spacer from silver stock or use available silver "findings" to make the caps. Findings is the word used by jewelers to describe the "parts" used in jewelry work, such as ring shanks, stone settings, clasps, catches, etc. Depending on the diameter of the jade, there is the possibility of the jeweler using "bezel cups" to make the spacers.
Bezel cups are stamped cups of silver (or other metal) used to mount stones onto bracelets, rings and other jewelry. Purchased, the bezel cups should work and will cost a fraction of the price if hand fabricated from silver sheet stock. Some silver design should be between each cap to allow the angle of the caps to match the angle of the jade ends for a clean look and secure fit. The use of a single section of silver tube for each spacer is possible but that depends on the angle of the jade at the cut ends and availability of silver tube of large enough diameter.
Yes, the job is certainly possible and not very difficult to do. The problem is getting the bracelet sawn in-two cleanly. After that, having the spacers made should not be a daunting task at all.
If you wanted, the spacers could be made one with a clasp and the other with a hinge, providing a bangle which opens and closes to be placed on the arm.
Joining the jade to the spacer cups (or tubes) will be cement designed for such work. I suggest fine quality epoxy cement which cures to a water clear color. One such cement is Hughes 330, designed for joining gemstone material and metals. Other epoxy cements will work just so long as the cement is applied with care with little excess to show at the caps.