Yes they do. However it is not 45 days. They are listed 26 days after expiry.
Example: "bwacp.com" expired on 14 Aug 2010. It is listed today on Godaddy. The page is here:
https://auctions.godaddy.com/trpItemListing.aspx?ci&domain=bwacp.com
It will stay there for 9 days. This is a public auction. Anybody can join at any time. After the time is over the domain will move to Closeouts (buy now). It will stay there for 6 more days.
All expired domains are auto renewed for 45 days by Verisign for free. This was planned to give the original owner a chance to recover. However the registrars are using this time to sell the domains.
Godaddy thinks any domain that is registered with Godaddy is property of Godaddy. Godaddy does not accept property rights of domain owners. This is written in their terms of service. They define domains as a service they provide. So this should give you an idea how things work in domain business.
9+6=15 days.