Probably not. There's a voltage difference between the Pentium 200 and the Pentium 200 w/ MMX tech. If your motherboard does not claim to support the Pentium w/ MMX (AKA P55C) then it almost certainly will not work.
OTOH, there are several other alternatives. Evergreen sells a variety of upgrade processors which should work in your motherboard. Winchip sells upgrade processors which should work in your motherboard. Cyrix might have something that would work. Possibly AMD K6 CPU's might work and you might want to look into this. I think your socket is called "Socket 5", and most of these want "Socket 7", but my memory starts to get foggy on these subjects, so I encourage you to look further into this.
Evergreen's products are usually a little steep for what they are (CPU's with a voltage converter built on), but they are a very good possibility for you.
Edit:
It's unusual for me, the AT Forum's unofficial Intel representative, to steer you towards an AMD product, but I would definitely consider the Spectra 400 for $130 at their page
here. This should work in your motherboard (although run their prequal program on your computer to be sure), and should offer you the equivalent performance of a K6-400 for $130 without requiring any changes except for the possibility of a BIOS upgrade.
I have no personal experience with Evergreen's products, but I have heard good things about them from other people.