Your computer is only going to access one at a time. Are you wanting to use one as a repeater somewhere else in the house away from the other router? If that's the case, you have to set one as 'router' and the other as 'repeater'. But they don't get wired together.
I would also not recommend it in this setup since the Netgear is simply going to outperform your U-Verse router in speeds. If you have dead spots in the home, I would set up something more similar to this:
U-Verse ethernet to Netgear.
Buy 2nd Netgear and use as repeater talking to Netgear #1.