I suffered from near-psychotic depression for a good few years and was suicidal. After i found out i had Dysautonomia, POTS and EDS type III, i made some pretty heavy lifestyle choices, dropped all my meds (i don't take anything, not even Ibuprofen), quit smoking & drinking completely (still drink coffee), fixed my diet (eating enough, but not too much. Healthy stuff, lots of fat and fibre) and i'm just amazed by the results. I haven't felt depressed in months. I swear. I was even committed to an psychiatric hospital and was an outpatient on three occasions.

So my answer to your question is: YES. Ehlers-Danlos can definitely cause severe depression and anxiety disorders through several mechanism. For example i was extremely malnourished and lacking in almost all micronutrients, which in itself is enough to cause psychological illness. Malfunctioning of the autonomic nervous system can manifest itself as symptoms that mimic severe panic disorder. Many with EDS have abnormal perception and may be more sensitive to loud stimuli compared to the general population.