I cannot speak for what companies do in general, but only speak from my own experience. In the beginning of my professional career I worked for a relatively large Danish company that was acquired by a huge multinational company. The acquiring company had a large group of fixed staff members who, almost like a SWAT-team, went in during the due diligence period and assessed the individual departments and teams from a cultural and competency perspective and this team also followed the integration process and worked continuously to ensure the integration of the target company. Once this integration was considered completed, the team went on to new, similar assignments in other areas. All of this was of course not known by us (on the target side) before after the deal had been announced.
Today, I work for a smaller scale company, but still multinational and here we are starting to establish a small group of people with focus on PMI to enable us to do more successful integrations in the future.
So to answer your question then, yes, I believe that many companies who have inorganic growth as part of their strategy will establish fixed teams with a PMI focus. I also believe that this tendency will grow even further as companies become even more aware of the deal value lost in unsuccessful integration efforts.