I could take multiple paths to answer your question here because I am not sure if you are asking of MS can cause problems with your back or if you are asking about lesions of the spinal cord. I am going to take a guess and tell you about spinal lesions.
Multiple Sclerosis is a demyelinating disease of the central nervous system which includes the brain and the spinal cord. So in answer to your question, absolutely, MS does affect the spine in that this is the place where lesions may exist.
In an article entitled, Multiple Sclerosis (MS) of the Spinal Cord, Brendan P. Coleman, MS states that: "In as many as 90% of MS patients, the spinal cord is involved. It is estimated that approximately 35% of MS patients exhibit spinal symptoms only. The cervical spinal cord is twice as likely to be involved as the lower levels."
When they begin the process of doing the diagnostic tests to see if you have MS, they will mostly likely do an MRI scan of both your brain and your cervical spine, which is basically the upper part of the spine including the neck area.
Some people have lesions only in their brain like me, some have lesions in both their brain and their spine, and some, as the stats above show, have lesions in their spine only.
There are many discussions on-line about which symptoms are produced by either brain or spinal lesions. Here is one such discussion.
Wanted to point out that I am just a patient who has MS...I hold no medical degree, so this would make an excellent question to pose to your doctor or neurologist.
Thank you for your question. I hope this helps some!