Both Sony and Microsoft this week have confirmed that their next generation consoles will wake up to remotely download new content when requested to do so.
PlayStation 4 will wake up when it detects you've bought content via the web, Playstation Vita or smart phone apps, Sony's Shuhei Yoshida stated on Twitter earlier this week.
Microsoft's Marc Whitten also confirmed this feature was also available on Xbox One. While on low power mode it will continue to download games and updates to remain always up to date, he said.
@SyriasSerj When you buy a PS4 game on smartphone, it will wake your PS4 up to start downloading the game. PS4 goes back to sleep after that— Shuhei Yoshida (@yosp) August 27, 2013