Weird. I was just contemplating this same idea earlier tonight because I'm trying to set up a photobooth for a party and don't want to spring for a legitimate ring flash.
I would think that if you had four flash units in a close enough square, then put them behind a circular diffuser, you might be able to closely mimic the ring flash look.
Why not mock it up before taking your flashes apart?
Also, I'm sure you know this, but in case you don't, be careful operating on flash units! Flash capacitors can hold a pretty nasty charge for a long time.