Yes, it can, or it could get worse if left untreated. Often chronic infections cycle, and some patients experience cycles of reduced symptoms along with cycles of increased symptoms. The increased severity of symptoms seemed to track with other problems, such as stress, trauma, etc. that can suppress the immune system.
It is my opinion that it is more likely to be other co-infections that do the damage. A very large segment of the population has EBV with no apparent symptoms. However, with the appropriate viral and bacterial co-infections this situation could cause CFS.