The answer you've been waiting for:
Since Laminar Flow and Induced drag have been addressed already: I will add my $0.02 about structure and substructure. A golfball and a wing are two different animals.
A wing is a stressed skin design which supports all imposed loads on its skin. Think of an aluminum coke can. You can stand on it slowly and it won't bend, but if it's dimpled even a little bit, you can bend it with one hand. This holds true even for our modern semi-monocoque wings with sub-structures.
Now a golfball is not a stressed skin design. The skin is not responsible for holding the shape of the golfball. This is true because golfballs bend like Beckham's soccer balls when whacked with a kinetic titanium club. I've seen slow-mo videos about it and I don't even consider GOLF a sport.
As Lt. Commander Data would say: "Theoretically it is possible." So theoretically if a wing were made of a solid core of fiberglass or styrofoam or even carbonfiber (like an RC plane) then you could put dimples in it because it's not the skin that's holding it up. But even RC planes are mostly stressed skin designs.
Now if you did have a dimpled wing; what would be the consequences? Well; assuming the dimples are placed on the top surface to speed laminar flow over the top of the wing, you gotta make sure that airplane never goes inverted. If it does, that plane will make a bee-line for the ground like a rock.
OK , so what? So I'll just keep it right side up! OK , but then how're you gonna certify the aircraft with the FAA? What about stall and spin recovery? If you're recovering from a spin, it already takes a coupla thousand feet; but with dimpled wings in a spin or an inverted spin, it's gonna take a lot of altitiude to recover (if at all) . ooooh, I doubt the FAA will certify the aviation equivalent of a dribble-glass! They have really dry wooden senses of humor those dudes...