I seems tight.
But, PSU ratings are not so much about absolute wattage at mains or overall wattage across all voltages as it is about the usage at a single voltage, most likely the 5 V in this case.
So, if that's rated at 15 amps here, that should still give you 15 x 5 Watts.
Then again, read up on the term "TDP" - it's about average consumption and cooling requirements, not maximum power draw. If the latter exceeds your PSUs capabilities for the split second, it's still no fun.
It's generally a big discussion whether it makes sense to use high-end AGP cards in older systems with older OS and games.
Instead of, say, a modest GF4 MX with rather negligible power draw.
If so inclined, don't know too much about ATIs, but there's a certain GF7600GT, that's a good mainstream GF7, which was produced in a smaller process of 80 nm and available with AGP:
http://hw-museum.cz/vga/205/gigabyte-geforce-7600-gt--80nm-
That is available with passive cooling, I assume this beauty is one, if hard to check:
https://www.ebay.com/itm/274727064318
So, that comes with a molex plug for the PSU, so it won't stress the mobo. One could measure directly at that cable how much power it draws at what voltage, maybe it's smart and uses the 12 V, dunno.
That's rated at 40 watts, which already is a bit of a stretch, but you can't hurt yourself trying it out.