The problem with the 'should fit' is that we really mean it 'should fit'..
One manufacturer's 225/40/18 tire doesn't always match someone else's 225/40/18 tire, and that is part of the 'should fit' problem. It doesn't matter if you have the sports package with good suspension, or not (ala sedan owners), the sports package (or PP, same difference) 'drop' is insufficent enough to worry about wheel rub more than any other 3 series.
So, you're back to the real questions:
What offset do you want/need on your new wheels, and what are you riding on already? (You could have 2 different wheels, both 18" x 8.5" wide with the same 245/40/18 profile tires, one might fit, another might not, depending on the offset of the wheel. IE: how much further does the wheel 'extend' from where it hits the axle)
and..
What wheels do you really want on there? Do you want the same size all around, or staggered? (This impacts your tire size, and 'what fits' under there)
and..
Do you plan to do any suspension changes in the future that might drop it further?
You can fit some huge tires under a BMW, and even bigger ones with a fender roll, or widebody kit.
In GENERAL - 225-245's will fit front, and 255-265's in the rear, on a non-dropped BMW. The variance is depending on the brand tire, and if it's a 'squared' or 'round' tire. Add a drop to the mix, you might be rolling fenders to keep those same size tires happy under there (and then again, maybe not).
I guess I coulda summed this all up and said 'there's no easy answer to your question' but thought some info to express this might be better..