I think it also depends on the scale of the integration effort. Many of the cases reviewed we are talking about relatively large companies acquiring small start ups and I believe it is safe to say that those kinds of integration efforts will not affect the entire company as new and very small entities will most likely just be swallowed by the mother-organization. If, of course, we are talking about bigger acquisitions I think there is a real chance of the organization experiencing what you are talking about – because when everything from HR and IT systems to work processes and organizational structure needs to be reframed, it becomes a completely different exercise.
Either way, I believe that much can be gained from having a designated team who works with the integration effort and who has well-defined interfaces and work processes allowing to communicate clearly and set expectations towards both newcomers and the old organization. When people feel comfortable knowing that someone has the details covert it creates a sensation of safety allowing them to focus on their jobs. If they feel that the integration effort is poorly handled or unstructured it creates noise and distractions, which can easily lead to fatigue. Well managed integration and communication is of course no guarantee that serial acquirers will not experience integration fatigue, but I believe their odds will significantly improve.