sure but it's better the M62 from the benz 230kompressor, as it's shorter and it has bigger displacement.
The Mini cooper S s/c has been fitted on a e30 by user "Appletree IS supercharged". Here are the pics: 
http://www.m42club.com/forums/showpost.php?p=58768&postcount=6 There was a member of bimmerforums, "frankie1000" that fitted it on a e36: 
http://forums.bimmerforums.com/forum/showthread.php?t=221624&highlight=frankie1000 but thread was old and pics are dead. 
IMHO the M45 has a big case, but small rotors, so that it will need a lot of space to be fitted and it will easily run out of steam. 
If you plan to do a such thing with a eaton, do it with the M62, at least it will have the same expandability as DASC. 
As you can see appletree is searching for a bigger supercharger, as he wrote that his m45 (the one from mini cooper s) is at maximal revs and can't do more than 8 psi... and if you know about eatons and their pulley ratios, they at max revs are pretty inefficiently (the air that the s/c send to the engine will be very HOT when high revving the S/C 

 )