Is it possible with TFS 2012 to use a build definition to run a bat file?
My application built on TeamCity by simply running a build.bat that did everything (Build, Test, Package, Deploy). I've tried looking online for a way I can run a build on TFS that JUST runs the build.bat (nothing else) but I haven't been able to figure out a way to do it using a build definition.
You should upgrade you TFS server to take advantage of more modern tooling. In TFS 2015 microsoft introduced a new build system that will do exactly what you need.
It has a task to execute a bat file and you can use that task only.