Yes, of course, many people have beloved pet turkeys. One poster on here shows a shot of his pet turkey perched on the open oven door each Thanksgiving, just as a joke.
The only issue comes if you have the broad breasted white or bronze breeds. Due to their genetics, they develop muscle mass far in excess of normal, or "heritage" breed turkey. As a result, they are prone to cardiovascular and orthopedic problems as they age. The best way to keep these in good health is to restrict the diet quite a bit to a bare minimum of calories to maintain a healthy weight, which is a actually a bit on the lean side, while giving supplements to ensure they get all necessary vitamins/minerals, and to encourage as much exercise as possible. Many people do keep broadbreasted turkeys for many years by following this regimen, but you should be prepared for the possibility that you may encounter heart/lung or joint/bone problems.
If you have heritage breed turkeys, they should be capable of living probably at least ten years. The broadbreasted birds seem to be able to live to five or six with proper care, sometimes longer. Its all about the healthy diet, not letting them overeat, and getting them to exercise.
Thank you for your service and sacrifice. I hope that you are able to enjoy your turkeys for a long time and find peace through caring for them. No reason I can think of that you shouldn't try -- there are plenty of turkeys for sale at the grocery store or local market each Thanksgiving, no reason you should feel like you need to give up yours if you enjoy their companionship.
