Can in the case of multiple sclerosis (MS), a too high osmotic pressure in the nerve, lead to a high intracellular concentration of potassium?
Firstly, demyelination has got nothing to do with membrane integrity of the neuron. Demyelination causes the current to "leak" through the ion-channels and thus causing loss of signal. 

There is an old article which reports a study on membrane integrity of RBCs of MS patients but there seems to be no connection. 

It has been proven that neurons do secrete some cytokines such as IFNgamma but the signaling is mostly para/auto-crine and I dont think the cytokines will accumulate in CSF. 

MS is identified by the presence of anti-myelin antibodies, which might be the exact biomarker for the disease. A general neuroinflammation is not concluded as MS. 

So to answer your final question 


  Is there research of this ?


There is none that exactly talks about neuron membrane dynamics in MS. The most parsimonious assumption is that there is no effect, but any hypothesis has to be proven. It might be experimentally difficult to address this question and how to design the experiment for this study would be an interesting question.