@ alx
With the aid of cutting equipment, quite a few new screw-hole mounting points, and a general cannabilism of the inside of the case, perhaps :-)
More likely an A500 though, the A1200 isn't that deep.
But even then, why would you want to? You'd have to throw out or adapter-ize 99% of the inputs between things like keyboard, drives, etc in order to manage it, and in the end you're only putting an x86 motherboard into a plastic case that says Amiga on it :-)