I don't think Tableau itself makes queries to mySql, rather it's internal repository is on Postgres. Also the admin guide advises against installing other apps on the same box as TS. It may work, but if it causes problems and you open a case with support, then they may point at this as a possible interference.
Jeff is right - Tableau Server should be the standalone app in the hosting server. Don't install db on the same server or performance may suffer due to resource contention. In fact, most people install Tableau Server on a different drive instead of the default C drive for further segregation.