In theory, Ms6852 has it right. A rotating bullet has angular kinetic energy (energy stored in the rotating mass). A faster rate of twist demands more energy be taken from the powder and put into rotation of the bullet. This not only uses powder energy, but it increases friction with the lands as it is done.
However, the above also assumes you are using a powder appropriate to the task. If the powder is a little on the slow side, that higher resistance can help it burn better, raising pressure and increasing the ballistic efficiency of the load (the % of stored energy in the powder that winds up converted to kinetic energy in the bullet).
Which situation do you have? The bottom line is, until you try a particular load in a particular gun, you won't know exactly what's going to happen. Due to variations in tolerances in the rifle and load components, you'll find you can't reliably predict the outcome. You have to measure. In most instances, something as small as a 1.33 fps/inch of difference in twist is less than normal shot-to-shot variation among your cartridges, so it fails to be a significant consideration in most practical ballistics. Kinetic energy of rotation is small compared to the translational kinetic energy (forward kinetic energy of the moving bullet) is much larger than the rotational energy.
For a 50 grain 0.224 bullet traveling 3200 fps and fired from a 9 inch twist barrel, I get 1137 ft-lbs of muzzle energy, and 3.01 ft-lbs of rotational energy or about a quarter of one percent of the total. If I change to a 12 inch twist, it drops to about 1.7 ft-lbs or 0.15% of the total. Converting to velocity, the 9 inch twist robs the MV of about 4.24 fps, and the 12" twist robs it of about 2.38 fps, a difference of about 1.85 fps.