Does sovereign nullsec space reduce the number of rats that spawn in their systems?

If an alliance claims a nullsec system and heavily invests in its infrastructure, does the number of NPC rats in the system reduce at all? I can understand if it doesn’t.

Quite the opposite, the pirate anomalies multiply beyond all reasonability due to upgrades to the infrastructure hub. Shooting pirates is an important part of upgrading your sovereignty and making your system more defensible – as well as making good ISK.