Can a 1600x900 resolution laptop still push 1080p through the HDMI out to an external monitor?

As you may have guessed I'm looking at buying the Yoga 13. I don't mind that the screen resolution is 1600x900, I'm sure it'll look very good. However, what about all of my 1080p movies and tv shows? My guess is that the CPU runs the media file at its resolution and then it's resized to whatever screen it's going to? Does this make sense? Can I still watch movies at 1080 through the HDMI out? Thanks in advance. Long live The Verge.