Are training systems considered operational? It depends. In a systems readiness point of view, yes, they're operational even if they've been re-roled, as opposed to being withdrawn-from-use or having another status.
But if you consider only front-line combat systems operational and exclude all other aircraft including training aircraft like the USAF's Texan IIs, then these wouldn't be included in that category.
Are training systems considered operational? It depends. In a systems readiness point of view, yes, they're operational even if they've been re-roled, as opposed to being withdrawn-from-use or having another status.
But if you consider only front-line combat systems operational and exclude all other aircraft including training aircraft like the USAF's Texan IIs, then these wouldn't be included in that category.