Ehlers-Danlos Syndrome is one of a number of genetic connective tissue disorders which manifest in a wide array of symptoms and as congenital degenerative conditions are not likely to change or improve. In these circumstances the best that one could hope to achieve with acupuncture would be to relieve some of the symptoms which are manifesting your particular case, and perhaps to slow down the progressive deterioration.
There have been attempts to use acupuncture as part of a package of measures to help people deal with the condition, but no research on the use of acupuncture with conventional treatment in contrast to conventional treatment alone which would allow us to make specfic claims. From a Chinese medicine perspective, however, there are a number of ways in which treatment is pitched at systemic problems rather than unique symptoms themselves, and sometimes ways of making sense of a collection of disparate symptoms in a way which Western medicine might not recognise. There may well be some merit in asking the advice of a practitioner local to you about whether the way in which EDS presents in your particular case makes sense from a different medical perspective.
One caution for possible treatment, however, would be the tendency to bruise and the effect on wound healing. Acupuncture is a remarkably gentle treatment, with especially fine needles being used at relatively shallow levels, and only in severe cases of blood thinning through illness and medication is it contra-indicated. Any practitioner worth their salt will always treat conservatively in cases like yours to gauge how well the body responds to the physical process of treatment.