Here is a manual for one of the versions of touchpads Comcast uses (they all operate extremely similarly.)
http://www.icontrol.com/support/manuals/technicolor/TouchScreen_User_Guide_TCA203_RevA.pdf
Page 5 has a network diagram of how it works
When Internet goes down -- Cellular connectivity allows only enough communication with central monitoring to communicate major events such as alarms.
Page 36 shows you a sample screen of what the test page would look like to test connectivity
The touchpad uses GPRS/EDGE with Verizon. You mention "awful cell coverage"...who is your current provider? THis could be provider specific so even though ATT lets say gives you bad coverage Verizon could be better....Also when a device uses GPRS it uses the Verizon cell towers but not like you think...it uses them for Data and a different kind of connection establishment than a typical Verizon cell phone would use. So what this means is potentially it could have an easier time to connect than a traditional cell phone.
Easiest thing to do is have Comcast out and just try the touchpad and use the wireless / cell statistics to get the best positioning within your house.
Hope this helps 