Theoretically, the board should give the right multiplier for all the PIII and Celerons. However, often the BIOS start posting the CPU speed wrong, although the CPU is still running at the right speed meaning it is working fine. (ie. Posting PIII 850 as 833).
CPUs drain more power (current) as the clock speed gets higher, and according to Intel, the original SE440BX does not generate enough current to support PIII500Mhz and higher. Therefore, although your CPU may run 1Ghz PIII, it may not be very stable (that?s what Intel says). Again, they are very conservative when they spec out their products. Therefore, I would not be surprised if someone like wetlan running PIII 1Ghz without having any problem.
I do not know which BIOS my SE440BX has as it is currently boxed up in my closet. You may just want to try with different BIOS yourself. I recommend getting FC-PGA version of PIII or Celeron, so that you can play with voltage/FSB setting (66Mhz or 100Mhz) on a slocket. For example, if one BIOS does not work with, say, PIII 750Mhz, you can switch FSB to 66Mhz and boot it up at 500Mhz (66Mhz x 7.5) and flash the BIOS to a different one and try again. Also, playing the voltage might help if the system becomes less stable. You just have to get a CPU from some place with good return policy and try it out.