No. If you have more twist than is needed, bad things start to happen. In extreme cases, the bullet can actually explode in mid air from too much centrifugal force. A bullet that has a 1/12 twist traveling 3000fps will be spinning 180000 RPM when it leaves the barrel. A light-weight bullet with that much spin will literally spin itself apart.
In less intense situations, you'll decrease accuracy. Not to mention an unnecessary hit to velocity (the more you spin it, the more friction as it goes through the barrel resulting in velocity loss).
Bottom line is that there is a theoretical ideal for twist rate for any given combination caliber/bullet weight. Since barrels cannot magically change their twist as you change loads, manufacturers have to pick an "average" that they think shooters will need. If you really do intend to use a bullet on either end of the weight spectrum for that particular caliber it will be to your benefit to select a manufacturer that produces a barrel that fits your intended bullet.
Case in point is the 30-06. The standard twist for that caliber is 1 in 10". You can get normal 30-06 bullets from somewhere around 140grn all the way up to at least 220grn. That standard 1 in 10" twist is ideal for a 165 to 180grn bullet. It will usually shoot 150's OK. However, if you try to shoot 220grn bullets, you'll probably find less-than-desireable accuracy. 1 in 10" just won't stabilize it well.
Manufacturers USUALLY get it pretty right. Remington has had some pretty ugly failures though. They developed a .244 (6mm) to compete with the .243. They thought shooters would want to use it with really light bullets for varmint shooting. They were dead wrong. Buyers really wanted to use it for deer and when they tried heavier (95grn) deer bullets, the thing shot like crap. Remington had to drop the .244. Later, they brought it back as the 6mm Rem with a faster twist rate. However, by then the damage was done and it was a flop in the marketplace. They goofed again when they gave their .260 rifles a 1/9 twist when the ideal .260 bullet (140grn) really needs a 1/8 twist. Savage goofed with its model 200 in 7mm/08. They gave it a 1/11 (I think) twist which is just too slow for that caliber.