That really depends.
Jack and the Gangsters reveals that while there's very little that can outright kill Aku, he can still be driven away if he meets stiff enough (not necessarily lethal) resistance like how the Water Goddess and her Elementals prevented him from stealing the Neptune Jewel:https://youtu.be/99UgZyPYcC0?t=55
So in theory, if Homeworld bunkered down and hit him with everything they had (magic, tech, etc.), they might be able to dissuade him from trying to take over; not worth the trouble and all that.
However, Aku's possibly geokinetic:https://youtu.be/tgCzKdKH0VY?t=68https://youtu.be/DXpGtGj5PkU?t=183
So that might be enough to give him an edge over any Gem that tries to give him trouble because, hey, they're still rocks.
In spite of being a twit most of the time, he can be rather devious and might see fit to destabilize Homeworld through treachery first before making his move; maybe even using bits of himself to take over machinery such as their ships and the Kindergarten Drills.
That's not even going into his other supernatural powers (shapeshifting, super strength, pyrokinesis, necromancy, flight, etc.).
It should be noted, that while he is a creature of darkness, light in general is not enough to hurt him (he fires it out of his eyes, remember?) so Gems being made out of his antithesis would not necessarily cause him much concern.
Something that could really hurt him? Steven (and perhaps Stevonnie) and maybe even Garnet since strongly concentrated positive emotions and virtues (Jack's katana is forged from the righteousness of his father's noble soul) can grievously wound him:https://youtu.be/87ZJp_mILAI?t=74