ANSWER: Yes. Although you may be unable to render "useful and efficient service" in your government job and are therefore disabled from it, you may be able to perform in a non-government job, and if you can, you are perfectly free to do so.
Example: Fern, an accountant, suffers from continuing bouts of clinical depression in part as a result of government job duties and long hours. Her symptoms include early morning crying spells, which often make her late for the daily staff meetings which are an integral part of one of the critical elements of her job. After she is awarded disability retirement, Fern finds a new job as an accountant in private business with duties and hours that she can handle. Fern is disabled from her government employment, and if she meets the other requirements, the fact that she can perform the private sector job does not prevent her from receiving disability retirement.