Uh huh they tried that it failed.
How many Exalted Marches have been led agaisnt the Imperium? How many have failed? 
About those Marches... they were conducted before Tevinter went solo against the Qunari by refusing the Llomerryn Accord. Tevinter has worked itself into an impressive stalemate, but it can't hold forever, and I really don't think the Qunari are giving everything they have. In the meantime the Qunari act as the perfect blunting agent. I imagine if there was enough interest from a united Thedas, attacking on Tevinter's opposite front could be quite effective.
Likely, if that were the case, whatever nations back-fill Tevinter territory (assuming a successful conquering campaign) would work themselves into the same stalemate position against the Qunari that Tevinter currently holds.
It is important to note I'd rather not have the Chantry involved, this wouldn't be an Exalted March. I would rather have rational best-interest be the driving factor, not religious fervor.
An extremely unlikely scenario, I know, but I can hope.