Notionally, it depends on the speed and load. The higher the speed and/or load, the more precise the C-C distance needs to be. If the belt is too loose, then at the higher loads, the tooth will ride up the cogs in the pulley and could skip. At higher speed, the “whip” of the belt will try to lift it away from the pulley - same effect, skipping teeth.
We discovered that we were using a belt that was 2 teeth too long on our shooter the other day, which is equivalent to the C-C distance being 5mm too short (or nearly 0.200" too short). The drive pulley was directly on the output of a NEO and the gearing to the shooter wheel was 1.5:1 (wheel 150% faster than motor). So, it was a high speed and high load application. There was a lot of slack in the belt but, surprisingly, it was working fine in the limited amount of practice shooting that we have done in that configuration. I would have expected that much slack to have caused a lot of problems. I don’t recommend that much slop by any means, but it certainly challenged my understanding of how much slack is acceptable in a belt at those kinds of speeds and loads. I expect that if we kept that much slack, we would run into problems over time and we fully intend to use the correct length belt going forward.