I suspect that a Qunari Invasion would have to start with the removal of the Imperium and the capture of Tevinter, otherwise it would have an enemy at it's flank and that hurt them badly during the last war.
But the problem with that is, the fall of the Imperium would likely be witnessed across Thedas, Antiva, Nevarra and even Orlais trades with them.
There really can be no surprise for Thedas, and that is something that would be critical for a successful Qunari Invasion, But the problem we face here is we do not know the number of ships the Qunari possess, nor their number of troops.
I couldn't even tell you if they have the logistical basis or manpower to conquer Thedas.
They failed utterly last time, in no small part due to just the sheer numeric superiority of Thedosians.
Oh I do not doubt that it would end in a sad failure (sad because a lot of casualties, military and civilian, would be incurred on both sides, not because I wish for the qunari to win, it is not a fun idea from a storytelling viewpoint). But I would like to see how it pans out nonetheless.
I agree that there is no way that the fall of Tevinter would go unnoticed but it does open up a nice possibility, much as I like Bioware storytelling it has always frustrated me that the people of Tevinter were always seen as these consistently evil types until Maevaris and Dorian came along. I don't like my villains, be it one person or a nation, to be so black and white. A Qunari destruction of the Imperium could very well do for their people what the Reaper invasion did for the batarians, showed that for the whole that the people were just as varied as everybody else but had suffered under a cruel government that seemed to revel in engendering hatred towards them. The one thing that saddened me most about that was that so many were killed for such a possibility to occur.
I think another reason that the qunari invasion may just fail is that as a whole what little we have seen from the Qun seems to suggest that they suffer from a crippling overspecialisation, as it were, and are not very capable when they are cut off from the rest of the body. That was witnessed by the people of the Free Marches, I doubt highly that any good military leader would let such vital information pass by them.