I feel no. I once accidently logged into my friends account (damn alphabetic order) on my home console and he got signed out back at his place (we talked about it on facebook when it happened), so I would think you get signed out of other Xbox One's if you log in to a new one.
I have heard of two friends setting each other's console's as home consoles, though. So I guess you could partially do this with two different accounts and kinda crossing the home consoles. Then basically both consoles could play any games, but I don't know if Xbox Video is smart enough to allow the console owner's videos to be watched.
So basically if you have a console in the living room and bed room, you could do:
Living Room: Logged in as secondary account, but primary account has set living room console as home console. This way anyone using the living room console gets access to all the games owned digitally by the primary account. Also Gold-account is shared to all users. Xbox Video/Music might share this logic, but I havnt heard about it or ever tried myself, so I cant confirm.
Bed room: Signed in with the primary account, this way you can play all games owned by primary account and watch Xbox Videos and other owned content most certainly.
That was just an example, it's not ideal but if you find yourself mostly just watching things in the bed room or mostly just watching in the living room, you could switch the arrangements around. You will be able to play anything on either console, but I think the Xbox videos will be limited to where primary account is signed in.