Yes! And it if it doesn't, you'll just want to enable that feature. ( It should be enabled by default) but if for some reason that was changed, just follow the steps below!
- Go to the System Settings by swiping down from the top once to open the menu, and again to expand the menu
- Scroll to Display
- Tap Display
- Enable Lift to wake
- Swipe the screen up to exit and now your remote should wake automatically when you pick it up