It's possible to polish anything, but its a huge amount of work. Usually raw aluminum rims are clear coated to protect the finish, so you would need to first media blast them to remove the clear coat, and then have them polished (friction + time + blood & tears).
You can also look for a local shop that does chrome plating, not sure what the pricing runs but I would imagine it to be pretty high for 4 rims.
Haven't looked at enough rims to know what's available in 5 spoke/polished that would fit an F30 correctly.
Current: '15 M235i Vert
Previous: '13 335i, '08 TL-S, '00 Corvette