I don't know why they wouldn't work.

One thing to consider is that the rear track of the M is wider than the
standard track. Having said that, the increased width could be accomplished
with the rims. The rims on the M are wider, with the backspacing the same,
so this would make the outside edges further apart which would make the
track wider. The track could be different due to supsension parts, but
consider that the parts have to bolt up to the same holes in the
undercarriage of the car.

What I did to my car (a 1994 E36, so there is a slight apples & oranges
comparison here) is to leave the suspension alone but I added 17 inch rims
from a '95 M3. I'm pretty happy with the handling and performance of my car,
but I wanted to dress up the lines a bit. Setting it up with 225/45x17s did
the trick.

Your car can hold a 235/40x17 on the rear with the correct rims, and
225/45x17 at all four corners without any alterations to the suspension. So,
if you need shocks and springs, go ahead and get them for your car and get a
better look with new rims.

I found my rims on eBay. Do your search for BMW E46 OEM <size> WHEELS (or
RIMS). Enter the size you want, or omit the size and get everything. If you
are willing to use aftermarket rims, omit the OEM. Personally, I'd not
select non-oem product for my car UNLESS I was going for a specific
application, such as for the track. I think that non-oem rims on a nice car
make the car look not nice. Maybe that's just me ...