Can poor circulation associated with thoracic outlet syndrome cause complications?

Depends: Depends on whether you are talking about true neurogenic as opposed to disputed neurogenic, venous or arterial thoracic outlet syndromes.

RISKS: If you have experienced artery or vein compression due to tos, and possess a cervical rib, there is risk of possible local blood clotting, and, on rare occasions, strokes have occurred. Since this can be very complex, and may be benign or more dangerous, best to have a very experienced thoracic outlet surgeon evaluate the blood vessels fully.