Unfortunately, I don't have any personal experience with Effexor, so I cannot offer you any specific firsthand information. However, I have heard of both Effexor, and other SNRI's like Cymbalta being used to alleviate some of the symptoms associated with POTS and Dysautonomia. Some patients are able to use these medications very successfully, while others are not. Like many of the other medications available, it really depends on the patient.
If you do choose to start taking Effexor, I'd ask your doctor about starting with a lower dose. Starting low, and going slow seems to be the best strategy for these types of medications. The biggest problem I'm aware of with Effexor specifically is that it's apparently difficult to stop taking after one has been on it for a number of months. Still, I would suspect it's worth a trying, most especially if it could be helpful to you. I hope you feel better soon!
Dysautonomia Treatments Page:
http://www.medhelp.org/health_pages/Neurological-Disorders/Dysautonomia-Treatments/show/171?cid=196