In Naruto shippuudden, when Sasuke and Itachi fought and Itachi died, if Naruto caught up with him before Tobi, would Sasuke have gone back to Konoha?

hmmm... dont think he would have. he's kinda stuborn and all...well, if they had reached him first, he would have been unconcious and they could have dragged him back, but i dont think he'd go willingly.

tobi convineced sasuke that danzo who manipulized itachi for the mission to kill all uchiha clan

Hmm, I don't think so.
I remember him saying that he would go find Madara Uchiha and kill him since he thought that Madara helped Itachi kill his clan.
So no, I don't think he'd go back to Konoha either way.
Plus, he's stupid and doesn't know it yet. -_-

he wont back, cause now he was trying to destroy konoha cause danzou one of konoha leader was told itachi about his revenge thing

1: yes is true sasuke he go back to konoha and 2: yes tobi want sasuke destroy konoha

and i love sasukee yeaaaaaaa i love himmmmmmmmmm