Archms: No, the overflow tank does not come with a hose inside it running down to the bottom. It literally was intended for race applications where the track wants you to have a container to catch coolant overflow. But here is a link to a site (under Craig's "tips" section of his website) that shows how easy it is to convert the plastic overflow tank to include the hose such that the tank will act like a true recovery system and draw overflow back into the cooling system as the car cools down. I did the conversion on my tank and it was quite easy to do.
http://craigscobras.com/
-Tim