According to Abit's website (http://www.abit-usa.com), the BX6 Revision 2 officially supports Pentium III 700 MHz (with the 100 Mhz FSB).
So it looks like it does support Coppermine P3's. I think it allows you to set the FSB to 133 as well, so you could even run one of the 133 MHz FSB Coppermines, but you said you weren't interested in overclocking, and setting the FSB to 133 will increase your PCI and AGP buses to higher than spec.
I haven't had any experience with this board myself, maybe one of the others could give you better info as to whether it will detect correctly and use the correct voltage. I wouldn't think it would be a big problem, though...