It TOTALLY can. My symptoms (head pressure, vision seeming "off" although I can't specifically describe how
it's off, perceived weakness in my limbs, dizziness) have been going on since July 25. Not constantly, but certainly more often than not and in varying degrees of intensity. I just went to the doctor on Wednesday, fearing I had a brain tumor, and you know what she told me? It's anxiety.
I don't know if you've seen any posts by Sixpack yet, but her signature line is great. What it comes down to is this - anxiety symptoms last as long as your anxiety lasts, and then some. They will only start to subside once your mind has been - and remained - calm for a while. It really stinks, but it's the truth. If you've been to a doctor and expressed your concerns about MS, and they didn't think there was any reason to send you for an MRI, you can relax. You're okay.
PS. I've been through the MS thing myself. Not for me personally, but my husband. He started having numbness and occasional blind spots a little over a year ago. I became convinced he had MS and forced him to go to a doctor. He passed his neuro test and as his symptoms haven't worsened and he hasn't developed any new ones, I'm trying to let the fear go. I'm about 90% of the way there. You can do it too...health anxiety is horrible. It takes work to overcome it. But it CAN be overcome! There are a lot of great people here sharing lots of great advice and resources. You're in the right place!