Rams are only aggressive towards conspecifics (i.e. other rams).
It depends on a lot of factors, I guess. How big is the tank, how many tiger barbs, etc. I think if you have enough tiger barbs, they'll pick on each other and leave the rams alone. Rams generally stay at the bottom of the tank. Barbs are more mid to top dwellers.
You'd probably be okay. Just watch them closely for a few weeks if you go for it.