Well, as I play Quake III on my iMac 350 (from 2000) all the time, I'd have to say that the answer is yes.
But beyond that, lets look at the minimum system requirements on the box:
- 3D accelerated video card with 16 MB of VRAM (it runs fine on my system with only 8 MB by the way)
- G3 processor running at 350 MHz
- Mac OS 9.0.4 or higher
- 64 MB of RAM
- 440 MB of hard drive space
- 240 MB of Virtual Memory
- Quad-speed CD-ROM drive
Plus, I've been playing Quake III on my iMac in Mac OS X since before Mac OS X v10.0.
I've attached a screen shot of my iMac from November 2000 when it was running Mac OS X Public Beta. You'll notice that there is a Quake III icon in the dock, that was the original Omni Group port of Quake III to Mac OS X (John Carmack took Quake III back in house for the final port to Mac OS X).
So, no, I'm not mistaking Quake III with any other game. And yes, I'm sure that Quake III can play on a G3 of that era as that was all that there was when it was released in 1999... and the system I've been playing it on since 2000 is just such a system.
For those who are interested, I also play Star Trek Voyager: Elite Force (based on the Quake III engine), Unreal Tournament and Ghost Recon on that system. I mostly play Ghost Recon though.
On a historical note, I still play Quake II on my Power Macintosh 7500 (with a PowerPC 604e at 210 MHz) running Rhapsody. As it turns out, Quake II was released for Rhapsody before it was released for Mac OS 8... and it runs better in Rhapsody than in Mac OS 8 too.