Will I experience any screen tearing?

screen tearing usually occurs when when the gpu tries to push more frames per second than the refresh rate of the monitor being used. assuming you have a 60hz monitor… you will likely notice screen tearing if you are getting higher than 60fps in a game. games all have vsync to battle this can introduce lag many prefer to turn off vsync off. some games can be configured to limit fps in games by locking in 60fps, 59.95fps, 59.94fps, etc.

so yes, any game the isn't demanding enough to punish the r9-270, and you turn vsync off, you will see tearing. with vsync on you shouldn't see any tearing.