It did for me, I felt like I was having episodes of ADD & Alzheimer's for awhile as well as many of the vertebral artery symptoms.
http://tos-syndrome.com/newpage12.htm
I was feeling really dumb for awhile...
I was also taking Lipitor at the same time frame, and it can play a part in the brain fog & extra muscle pain. When I quit the Lipitor I began to feel more normal, but at the same time I was finally getting some good PT & good chiro care. So not sure what % was from TOS or the Lipitor.
Many other conditions can cause brain fog too - as well as medications