Can internet sharing (Ethernet->WiFi, 10.6.8, iMac) extend an existing WiFi network from an AirPort?

I want to leave my AirPort Extreme (version 76400.10) at one end of my house, and use my iMac with Internet Sharing activated at the other end of the house. Ideally, I would be able to walk around the house with my phone and seamlessly connect to whichever access point has the better signal. I was told this could be done if both networks have the same network name and password, but I'm having trouble setting it up. I have both Airport and iMac set up with the same WEP password (WPA not available on iMac internet sharing).

Still my phone insists that there are two separate networks and doesn't magically stay connected to the internet as I walk around without manually switching.