Is it possible to develop a plug-in for Internet Explorer that can replace the existing favorites functionality?
Absolutely, however, it does depend somewhat on what you expect "replacing" to mean. You can develop an extension to provide a new set of menus or dropdown toolbar of some kind like the Google Bookmarks toolbar for example, or like the Delicious toolbar & sidebar. These IMO are much better designs for managing bookmarks than the built-in IE menu anyway. However, you could build a top level menu structure that worked the exact same way as the IE favorites menu if you wanted as well. There are many libraries out there that you could use to even handle the IE integration as well.
I don't know what language you develop in, but some example libraries to make the IE addons a breeze are (for .NET, there are plenty others out there for other languages as well):
http://www.add-in-express.com/programming-internet-explorer/
http://www.ssware.com/ezshell/ezshell.htm
also some articles to create your own from scratch:
http://www.codeproject.com/kb/applications/codeprojectsearchbar.aspx
http://www.codeproject.com/KB/atl/rbdeskband.aspx
That should get you going.
