Climate is also a known factor. MS is more prevalent in temperate climates. A study from some years back suggested that if you move before the age of 15 or so, you get the risk of your new climate instead.
Long answer is that the question is premature (we need to answer more mechanistic questions first, and then we need to have an actual potential vaccine strategy to talk about) and there is currently no particular reason to suspect this.
The immune system upon reacting to EBV or a vaccine should theoretically eliminate EBV on contact so it won't stay in your body?
Are you implying that that a vaccine cannot eliminate EBV?
Additionally, a faulty immune response also means your immune system can't differentiate between EBV and your nerve cells. So theoretically speaking even if there's no EBV in your body having MS means that your body thinks EBV is in your body even if it's not. A vaccine in my mind could still induce this reaction.
There are obviously other causative factors influencing MS. One is EBV, the other is likely a specific type of immune system.