I doubt it. I don't think the AGP version would be much more power consuming than the PCI version.
I did a search for "HP Pavilion 8575C" and it says it has a 550mhz P3. It's hard to find the actual power output of individual processors, but Tom's Hardware found (
here) that an AthlonXP 2100+ consumes a maximum of 89.88 watts of power. I can't see the P3 550 consuming even half the power of an AthlonXP 2100+, so let's guess-timate the P3's power output at 40 watts.
Add 28w for a hard drive, 23.5w for the motherboard, 19.2w for a media drive, 20w for two memory sticks, another 25w for keyboard, mouse, sound, USB, etc. and an extra 10w for "fudge factor", and you have 165.7w of maximum power consumption (excluding graphics). AMD suggests that the power supply needs to be able to handle 100% of the processor power consumption, plus 80% of everything else. That would mean the above list (which still doesn't include a graphics card) would need a minimum of a (165.7 - 40w processor= 125.7; x0.80= 100.56; + 40w processor=) 140.56w power supply, leaving you with 45w to play with (though you wouldn't want to go right up to around the 185w mark). For perspective, Tom's Hardware has a GeForce4 Ti4600 listed as consuming around 30w at max power, and supposedly the Radeon 9700 Pro's max power tops out at around 54w.
A Radeon 9000 should be fine, and the whole setup shouldn't stress a 185w power supply too hard. Since it's a 550mhz processor, any faster graphics card would be bottlenecked by the processor anyways, so I wouldn't bother going to a more powerful card than the 9000 (you'd just be wasting money).