The current barrack system has a single queue for all troops be it elixir troops or dark elixir troops. I know how the training time is calculated and all the other stuff. I would like to know what would happen if I decide to upgrade both dark barracks at the same time. Will I be able to train dark troops as there is a single queue for all troops or I won't be able to train any dark troops?
You would not be able to train dark troops while your dark barracks are upgrading. You can train normal troops from the normal barracks.
From the coc wiki: barracks will not function while under upgrade. http://clashofclans.wikia.com/wiki/Barracks