Is cork an effective solution to reverberation problems?
No, not by itself. You're dealing with a spectrum of sound, cork will only partially absorb a portion of the spectrum. It will certainly improve things, depending on the existing wall surface. Also, don't forget the ceiling contributes more to reverberation than the floor.

Absorbent materials is one way to control reverberation. Another is altering the surface angles to eliminate parallel surfaces. This is why many concert halls have those odd zig-zag wall surfaces. This is also why heavy draperies are effective, besides significant absorption, what sound is reflected is done at random angles. It's certainly debatable whether these treatments are attractive or not.

You would be best served by using a variety of strategies to better address the full sound spectrum. Do not rely on one material, use a variety on every surface. Anywhere you can, even if in only a few spots, disrupt the straight walls with something with different surface angles.

Corners are also strong reflectors. Placing tall architectural or sculptural elements in corners would be beneficial. Also consider the wall/ceiling corners. Certain indirect lighting or sizable crown molding in this area will also help. While you wouldn't want a totally random hodge podge of materials for aesthetic reasons, a tasteful variety would be more attractive than every surface covered in cork, IMO. I like cork too, but not on everything! :)