I played as Jozai on Hard with battle realism, after i won my first campaing (that was on legendary) i never ever returned back to that difficulty, because i only find it more tedious and not more challenging than a hard campaing. Therefor im also very confident that its possible to do this in a legendary campaing, also you could create a republic (i stayed loyal to mr. shogun), however you will probaly have to run on normal/high taxes and recruit units from most of yours cities (good thing theres a master dojo in all of them!) instead of only in the province with the legendary dojo as i did.
I can only imagine how annoying it will be due to how autoresolve rates traditional units, in my campaing i slaugthered armies of 7000+ men with 500-700 loses, but autoresolve will let my armies lose 300+ men to simply just kill of a few battered units.... Thus on legendary you will probaly wish to figth every got damn battle.