Yes of course they can and they should as long as they can, with supports and services. It helps if the position is flexible on hours, does not involve standing for long periods, working in a hot or cold environment, and limited lifting.
Jobs that allow for movement.
I can no longer work and gave up a top notch career. The most devastating part of EDS is having the choice to work taken away. I could no longer choose to get up and push through as this disease finally made it impossible to push through. However, what was hardest is being recognized as a person that still has a brain and can still contribute to society. Help the person with EDS to easliy get the supports needed and the alter or tweak what they already know, and conform the position to work from home, be their own boss. Again, education and knowledge are vital to helping ourselves and others to understand how to live, treat the illness when things go 'south' as they do, but still be able to feel like a part of life. EDS can be very isolating even in a crowd of people. Invisible illnesses (such as this one) can isolate someone and reduce their sense of self worth quickly, which starts a cycle that can destruct their physical health and mental well being.
Having a job, keeping a career, going back to school....ALL so important for everyone, and it is not always available to everyone. But it should be.