Sort of. In tumult's case he's got a connection that's actively downloading data and playing music. I would assume that'd keep the radio chipset (either wifi or cell, whichever he's using) and the CPU both from being able to switch to a lower power standby mode.

However, you can have an open but idle connection open in the background with only minimal battery drain. That's how pretty much every kind of push notification or IM system works, even on cell phones.