Their lack of AI would deny them a huge advantage, in that they would not be able to effect the (arguably) easiest form of invasion and seizing control. With an AI they would never need a ship to invade. Instead, all they would need is some bandwidth to transmit it over. But since they don't like AI, they wouldn't actually be able to successfully invade as I could see.
In a planetary invasion the natives are at an overwhelming advantage over any would-be invader, due to sheer number of people in militaries (let alone the hordes of shotgun-armed Texans.) To actually invade a planet like Earth successfully, they would almost definitely need an army of at least ten billion personnel. I highly doubt your fleet would have that many people.
Alternatively, they could destabilize the world's governments through insurgency. This would be (relatively) simple: use social media to make a population discontent, and then use this as a jumping board to incite rebellion on a global scale. Wait until ANTIFA, ISIS & Co. have established global anarchy, then have your aliens come as saviors. Do a global COIN campaign, then rise to power through humanity's own political process.
Takeover complete.
