I tried hooking my Coax cable from my uverse gateway to a tv tuner and I got nothing. So my guess is no. They should still offer limited channels without a box just like comcast does. They are greedy and just want you to pay the extra $10 a month for an extra box.
Without knowing the specs of the card that came with your computer, it may not handle what UVerse is sending.
Additionally, if the signals are scrambled you would need the U-Verse set-top-box to descramble them and *then* send them to your PC. The only channels that would be let through would be unencrypted QAM channels, which would be your basic over-the-air ATSC/NTSC channels. And even then, maybe.
Like skidabump said, they'd prefer you rent another set top box!
A tuner card would be of little use with Uverse because there are no channels in the traditional sense; the data is all digital and all packets, much like the packets that are sent on your home network, and the channels are no longer separated by signal frequency. This is not to say the /signal/ is digital -- it's analog and has to be demodulated (like DSL) -- but the /data/ is. Uverse resembles a computer network more than a cable service. There is a reason for that -- they are less encumbered because they no longer have to follow cable legislation since they are not legally a cable provider. The cable provider that supplies my apartment complex has also circumvented cable-provider law by directionally broadcasting their signal to a receiving station with an antenna built on the property. Since they do not use a public conveyance (the buried cable), they are legally not a cable provider. My cable company asked for a waiver and were granted one, just because they send their signal differently. You write your own rules when you are not classified as a cable provider. One of them is you can encrypt everything, and the majority of at&t's content is encrypted. There is little reason to tap into their signal if you cannot decode it. The other major rule they get to circumvent is sharing of their network. It appears they want total control of their network, and as little regulation as possible.
Interestingly enough, the video format at&t chooses to transmit in is a common format that many video files you find on the web are distributed in: H.264 (mpeg4 avc). Except at&t encrypts it. When you download a torrent file there is a good chance it is in this same H.264 format. (Some of you will have their ears start to tingle about now.)
This different type of broadcast network that at&t has chosen means they are only able to transmit one or two High-Def channels to your door, since that maxes out their bandwidth capability on the last mile of their network. [The service will be like one High-Def combined with one Standard-Def, or two compressed High-Def.] This means that some type of set-top box is required to not only decrypt and demodulate the signal but to tell at&t which channel(s) to transmit, because they cannot send them all to your home at the same time. There is just not enough bandwidth. When at&t decides to extend their fiber network to your door then that will change, there will be essentially limitless bandwidth, but in most instances I don't think that's the network structure at&t is rolling out. Verizon appears to be taking this later approach and using 100% fiber. If you have multiple TVs on at the same time in your home, I can see a lot to like with the Verizon approach.
Conversely, even though the Uverse network is limited in the number of channels that can be concurrently sent to your home, the digital network means it is easier to quickly switch content. In other words, you will likely have a much larger selection.