Of course - that could happen (eventually) and YES - that would save money for Tipton and Tri-Central, if Tri-Central and Tipton are both willing to explore this option. In this situation we are assuming both schools would be willing to merge like Frankton and Lapel merged. They maintain their individual campuses and have one central administration and one Board of Education.
The issue still remains that on some level, neither Tipton or Tri-Central are looking to merge. If you think they don't want to consolidate now - if we are talking about merging JUST administration, that conversation won't happen willingly. Nobody is going to initiate a discussion about how their job could potentially be eliminated.
It also is true that any school consolidation is a process that takes time. It does not happen overnight. It doesn't happen in a calendar year.
Merging administration - changing the name of the corporation to Tipton County School Corp - WOULD save some money through staff attrition. If you want to discuss a much larger potential savings, you will want to discuss closing a campus.