When I mentioned connecting using Ethernet, I was implying that the AirPort Extreme would be located some distance....a few rooms away at least....from the Uverse router. You would have to figure out how to the get the Ethernet connection from the Uverse router to the AirPort Extreme and then configue the Exterme to provide more wireless coverage.
IF...the AirPort Extreme is an "n" version...AND.... the AirPort Express devices are "n" versions....AND....you would be willing to turn off the wireless on the Uverse router and use the AirPort Extreme as your main wireless router, it could be located very close to the Uverse router.
Then the "n" AirPort Express devices could be configured to "extend" the wireless from the Extreme.
Bottom line in this configuration is that you would be using the Uverse as a wired only router.