Visited November, 2011. Oficially off limits to foreign tourists due to security reasons but you can try to get permit in Turbo (NP headquarters). There is base for scientists in Sautata (access by boat only) - very basic standard but at least you are on National Park premises ....
Unoficial and the only possibility to see at least some parts of National Park without any permits is to take a boat Turbo-Riosucio and in Riosucio take collectivo back to Turbo via bumpy road (the same day). During your boat trip there will be a chance to see Los Katios from Atrato river