In terms of deducting history, Conan is more likely to deduct general things unless someone specifically asks him to investigate a specific event or question. He'll have no problem figuring out that Kenshin had fought in a war, that he's very accomplished in some discipline of swordfighting, etc. He might be able to connect it to the Bakumatsu eventually, once he actually accepts that people here might be coming from other times. He did solve a case in his canon that was related to the Meiji era. But probably won't be able to make it any more specific than that.
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In terms of deducting history, Conan is more likely to deduct general things unless someone specifically asks him to investigate a specific event or question. He'll have no problem figuring out that Kenshin had fought in a war, that he's very accomplished in some discipline of swordfighting, etc. He might be able to connect it to the Bakumatsu eventually, once he actually accepts that people here might be coming from other times. He did solve a case in his canon that was related to the Meiji era. But probably won't be able to make it any more specific than that.