Enton Kagutsuchi is his ms tech with that ability. Irrelevant example as what you are comparing isnt the same thing. Without that line of reason there is no reason to believe that Sasuke can use Chidori or any other tech with his Susanoo.
Kakashi could only combine Kamui with the Shuriken due to the power he got. Naruto could only use BDFRS with the power he got.
Enton Kagutsuchi is him manipulating the Enton. His Enton which merely appears on his Susano is not a Kagutsuchi
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. His right eye only shapes the flames, it does not cast them. Being an MS technique does not change anything, it's simply a KKG element and it has nothing to do with his ability to channel it through his Susano unless you can back up this claim. He's used it as if it was a regular KKG when he manipulated it with his hand [
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]. And anyways, without that line of reasoning we can still suggest he can do it because he did it at VOTE2. VOTE2 granted him nothing which would give his PS that ability. All he got was Rikudo chakra which increased his overall ability to fight, which doesn't mean he gets the ability to channel Raiton through his Susano. It didn't open up Tenketsu which were previously not present or anything of the like.
Kakashi only being capable of using Kamui Shuriken because of Rikudo chakra is an assumption. Only argument you can make is that without Rikudo chakra it wouldn't have been anywhere near that power because of the Rikudo chakra potency boost. Had he had PS without Rikudo chakra it could've been a possibility as well for him. And anyways, even if he couldn't, that doesn't change anything since it's not a chakra nature in the first place. Naruto could only use BDFRS because of his increased increased chakra control, and the fact that he received Gudo Dama which he didn't have before. Sasuke's situation is nothing like this, he's already shown chakra control when manipulating his KKG element through his Susano and he's used Enton's which have the same chakra amounts as COFRS without being phased by it. A PS Chidori on a weaker level (due to the lack of Rikudo chakra) is definitely a possibility.