There is a remote chance of spread from an infected AI. Upon spread, it would impact you normally.
The AI has a get out of jail free card in that the setup doesn't cycle. The disease will progress normally on the infected planet, with small chances for the disease to spread to planets via trade ships that get infected as it grows, but the ship infections happen on the cycling of each stage. For the AI, those fire once, and only once. Infected trade ships might pass the disease on, but they're finite objects with a 900 second life after infection, and only a 5% transmission rate at each jump.
During implementation, I saw one to three planet infections in test runs to see how the AI would be impacted.
Minor factions are indeed different.
With the currently existing factions, you actually conquer them and take the planets, then you get the persistent starbase and can get access to features with tech upgrades.
Minor factions are instant acquisitions. Move an envoy into the well, and instantly gain the defensive position. They won't be coming in Tamarian and Son'a variants due to that ease. As such, they're generally less substantial threats. They'll give you some sort of useful tool, as well as a relatively cheap point of defense, with the low ceiling making it an ineffective bulwark in the late game compared to a fully maximized player owned planet.
Colonized Neutrals will be high end property that can yield a late game advantage by comparison.