If Overwatch works like Diablo 3 does, you can just add it to the Steam library as a non-Steam game, just find the Overwatch folder and add the .exe file.
Playing the game outside/without logging on Battle.net wont change anything as far as I know, you just will have to enter with your Battle.net account when the game starts.
I would. If I had Overwatch. The game is a bit overpriced here, the local price doesnt matches the exchange rate.