Yes it will tear if you don't use vsync and let the framerate go wild. Bottleneck? I mean I guess you can use that word because the 1070 paired with a decent cpu will easily do well over 60fps max settings in many games, even 1440p well over 60fps in a lot of games. So you won't really tapping out your 1070 at 1080p 60hz with vsync on.
EDIT: Vsync is available from the gpu, the monitor does not have to support vsync. To use gsync you need a compatible monitor, not vsync.