A lot of people here have both Battle.net with retail and the 1.12.1 Nostalrius client running on their computers. They don't conflict with each other as long as you keep them installed in separate folders. In my case, I've got a folder on my E:\ drive with all my retail Blizzard games and a separate folder for the Nostalrius client installation.
Worse thing that can happen is if you accidentally setup your Battle.net client to include your Nostalrius folder, the WoW launcher will try to update it from 1.12.1 to the current patch 6.2, but other than that, nothing to worry about. Go to the following link if you want more information:
https://forum.nostalrius.org/viewtopic. ... 40&#p68566