It doesn't seem like this will change much. Loyalty is still loyalty, it's driven by far more than packaging.
Case in point, in NYC when packs were no longer allowed to say "Light" and were forced to switch to "Gold." People would continue to walk into bodegas and convenience stores and ask for Marlboro Lights, get handed the gold pack, and walk out. I feel it'll be the same even if the branding element is removed.
In fact, it might make "your" brand even more significant, because you have to be asked about it rather than it being something that's just visually acknowledged.