Will it work? Yes, if you install the multimedia drivers for it.
Will it look good? Probably not.
I would probably spring for one of those capture cards based on ATI's new RageTheater capture chip (forgot which model - 200? 500? Whatever their newest one is), although if your budget is nearly-zero, then that won't do.
Some of ATI's newer AIW video cards can use their DX9 shaders to "clean up" video (ATI's "VideoSoap" feature), which is supposed to both enhance the visual quality of the captured material, and enable it to compress better. (Less high-freqency noise artifacts in the video stream.)
I have a WinTV PCI (older 848-based model), which is probably on about the same level of quality/features as the original ATI AIW cards. (Used to have one of those too.) I'd say that capture quality is probably a bit *lower* than that of a decent four-head VHS recorder on decent-quality tapes.
I don't know if you are taking about the ISA or PCI version of the ATI TV Wonder VE, but the quality of the old AIW (Pro) is pretty-much similar, IIRC.
For $50, you can get a much more modern PCI capture card, and some of them even have hardware MPEG encode/decode features. ("PVR" cards. Hardware-based MPEG is not so great for editing, but is fine for just bulk recording/playback. Otherwise, spring for one without hardware compression, but one that has 10-bit ADCs for each R,G,B color channel, and can capture at full broadcast NTSC frame sizes at full frame rate. Recent PCI cards can do that. Don't forget, you'll need plenty of HD space, and a fast HD/controller too, and/or a fast CPU, depending on whether you capture, and then later encode, or if you encode in realtime as you are capturing.)
The problem is that this is already a generation loss from recording the original source onto VHS, and then there will be a generation loss during the capture process, and then a further generation loss (controllable) during compression. By using a better capture card (with 10-bit ADCs), you minimize the generation loss during capture, and by doing the compression in software as a secondary step, you can use high-quality multi-pass encoders to minimize the generation loss during the compression step. But that does take a good amount of HD space and a powerful CPU.
OTOH, you could simply just
try the ATI AIW card, using their own ATI Video compression codec, or standard MPEG-1, and see what the quality is like, if it is acceptable to you.
Update: Check out
this thread. It talks about that new ATI capture chip, and some other various capture and PVR-style cards.