Pretty interesting question if one limits it to just 'mileage'.
If you believe there is 'efficiency' that BMW has left on the table, then a tune COULD eek out a bit more power (at a given rpm) and therefore deliver the needed power with a fraction less fuel.
If you believe that.
There is no 'free lunch', but there is little 'slop' in this proicess. Manufacturers DO trim back a BIT, to create a safety buffer: At WOT, approachiung redline, they dont want the motor leaning out dangerously. A tune will typically reduce these safety factors- more advance, maybe lower AFR, and get those 'peak HP dyno numbers' that everyone needs to see. HOWEVER, at cruising speeds (rpms) there is even less room to optimize.
At the end of the day, I'd expect even less mileage difference than you'd get using 91 versus 87 octane.
Surely not enough to screw with a warranty, and never enough to make it financially wise.
Keep it as simple as possible...but no simpler.