The highest they ever made was a 3200+.
Geforce 6800 Ultra 8x AGP 256mb
With an 8000 or newer series, Youtube videos
should play fine. AGP leaves you in a bit of a bind, though, so if you want to get a video card, trawl eBay.
It wasn't that long ago I was doing 720p on P4 Northy @ 3.4ghz. That had HT, but my gfx card was a Ti4200.
Edit:
That was also running Ubuntu, which generally has poorer Flash performance than Windows.
This is Windows, though, and if it could handle it, then no, it did not have poorer flash video performance

. Youtube plays choppy even with low-end Core 2 Duo CPUs, w/o hardware decoding, today, which
should leave that P4 in the dust. Overall, web browser flash video playback is the
one thing 
that people with basically no performance requirements can't do well enough on old hardware. Non-web playback is fine, usually, just with some dropped frames, but flash video players need hefty CPUs, or dedicated hardware to call. An AGP 8000 series or newer Geforce from eBay
should take care of that, of course.