I've tried a 7600GS AGP in a few games with a P4 CPU, the most demanding were Skyrim and Fallout 3. Skyrim was definitely slow, but if I was living by the standards I had in the 90s I would have played it that way.
Fallout 3 was pleasantly playable on low settings IMO except for combat. That's unfortunately a problem with the design of F3 - it's framerate requirements are all over the place depending on the situation and it doesn't auto adjust details to compensate. I wonder how much the CPU might be a factor in combat though, with all the AI activity that's taking place.
In those games I found that the main limitation is the shader performance. They respond more to overclocking the GPU clock than they do to the RAM clock. I assume this is the typical bottleneck for later games on GF7 cards. Surely the P4 CPU was also a limitation though.
The 7600GS works well with FlatOut and FlatOut 2, but those games aren't as recent either.
I haven't tried Mount&Blade/Warband, but from searching it looks like it will work.
Unlike my older cards (not sure where the cutoff is), the 7600GS is compatible with Faster Than Light and Terraria. I haven't tried any other modern indie titles with it. Many of those aren't very demanding but they can have the issue of requiring modern API versions. I would guess the GF7 cards generally have a good shot at working with indie stuff from a few years ago like the above titles, and maybe even recent titles (I haven't looked into it much).
I just looked up Darkest Dungeon and it looks like sadly that won't work. It's written for OpenGL 3.2 which according to an nVidia driver note appears to require a Geforce 8 series, which conveniently isn't available in AGP.
I haven't bought DD yet but it's the type of game I was hoping to be able to fire up on my older machines, not just the modern one. With WinXP support and syncing via the Steam cloud, it almost achieves that, so the late OpenGL version requirement is a bummer.