Normally the nose of the bullet casts about 8 thou less than the body. So your .313 bullet will size down to .309 or whatever on the main body but still be .305 on the nose. So it depends on the lead-in to the rifling. If the nose engages with the .300 lands on the bore when the cartridge is chambered, it won't go in easily. Might do weird things with pressures- someone here will know.

If it chambers easily, with no rifling marks, I can't see there being a problem.