I just don't see enough evidence for a direct correlation between the construction of the veil and stopping the Blight... **shrugs shoulders**
Although I believe that it would be exceptionally cool for Arlathan=Black City, I think the canon lore that we have, unfortunately contradicts that. According to the timeline in WOT, the quickening (caused by construction of the Veil) was first noticed in -2850 Ancient. The fall of Arlathan occured almost 2000 years later, in -975 Ancient.
I plan to reply further in a bit...
What if Arlathan was like the Vir Dirthara, parts of it existed in a pocket dimension or floated in the sky. Arlathan may have been partially destroyed or moved into the Fade when the Veil went up, that doesn't mean the survivors didn't rebuild in the ruins in those two thousand years after they became mortal.
Edit to add: The Veil primarily was created to contain to restrain the Evanuris. The Evanuris, it has been heavily suggested, were using blight magic and threatening to unleash it on the world. Abelas said that Arlathan was already a desiccated corpse by the time the Tevinters rolled in, already long diminshed. Whatever they destroyed may not have been all of Arlathan.