Apple - Keep wi-fi connection while asleep?

If your Mac enters its full sleep state, then your network connections will be disconnected. Your Mac can not be connected to a WiFi network and be asleep at the same time.

You can avoid full sleep by setting your Computer Sleep to Never. Your MacBook will then sleep all the sub-systems possible when idle, but will remain awake enough to maintain a WiFi network connection.

PowerNap is not the same as full sleep. This is a special state controlled by Apple and, for now, available only to Apple's chosen processes.

See where System Preferences -> Energy Saver says:

Wake for Network Access? If your mac is asleep it can still be accessed via Wi-Fi, and woken up.

Power Nap wakes up and connects to services and then disconnects, going into Bonjour Sleep Proxy mode for being woken up again via Wi-Fi.

http://support.apple.com/kb/HT5963

http://support.apple.com/kb/HT3774

One thing to note tho, when Power Nap "wakes up" for the brief moment, the screen does not wake up...