It depends on the bullet design. How far the center of gravity is from the geometric center of the bullet's bearing surface determines how far each thousandth of bullet tilt will move the bullet center of gravity away from the bore axis. If a double-ended wadcutter, there is zero difference, so tilt doesn't affect them. For long bullets where the center of gravity is further forward of the bearing surface, it is significant. A. A. Abbatiello's old article in the Rifleman in which he measured runout and fired 829 rounds from forty-two lots of National Match 30-06 loaded with the 173-grain, seven caliber tangent ogive boattail bullet with long boattail and 0.89 caliber bearing surface. He found the group radius increased about ⅛ moa for each 0.001" of bullet tip tilt (try saying those three words ten times really fast) up to 0.0045" of tilt, beyond which additional tilt made no difference because the bullet would straightened greater amounts down to 0.0045" of tilt in the bore. In other words, the the diameter of the group could increase up to 1⅛ moa.
Abbatiello references a similar study with similar results by George L. Jacobsen of Frankford Arsenal, published on page 20 of January 1960 issue of American Rifleman.
Shooting a 68-grain 6 mm flat base bullet,
Harold Vaugn repeated the experiment but got only about 40% of the radial dispersion Abbatiello got. However, the bullet he used has a longer bearing surface (in calibers) than the 173 does, so it will straighten a bullet more. It's just important to note how dependent on bullet shape the effect is.
Abbatiello said between 20% and 30% of bullets in the boxes were tilten by 0.003" or more. If you read the two pages on Vaughn's experiment, you will find that by always pointing an equal bullet tilt in the same direction in the chamber, the error and its direction remains the same. So if you have commercial ammo and sort it by runout, you can intentionally shoot groups oriented 180 degrees apart in the chamber and see the worst case effect of random orientation. Then shoot the same number of rounds all tipped the same way, and you will get a group the best size you can expect from the ammo. Abbatiello noted that if all he did was mark the high side of all his cases and always oriented them the same way in the chamber, he cut groups roughly in half as compared to letting them be randomly oriented in the chamber.