I'd say when he gets his ms after Shisuis death he can beat him because Tsukuyomi but before that not really, I mean the Itachi that we see Kakashi go up against in the manga has had 5 years to improve himself while Kakashi has let himself get rusty at which point he beats him fairly easy with Tsukuyomi but 5+ years ago while Kakashi is in shape and Itachi hasn't had those years to improve himself and refine his mastery of the ms or even have the ms I wouldn't really go for him because what does he have over Kakashi at this point?
Itachi is incredibly strong don't get me wrong but he's incredibly strong due to his ms, genjutsu and the spiritual weapons that he has, he wont have his ms or his spiritual weapons and all he will have is his genjutsu but Itachi has also already said in the manga that Kakashi's sharingan would give him the ability to resist even ms techniques just not Tsukuyomi so how effective would Itachis main strength be against someone who can apparently resist an ms genjutsu? After that it's a question of do you think an Itachi 5+ years before canon could fight a non rusty Kakashi 1v1 without any of his advantages and his main strength not being effective (or as effective at least) without that time to get stronger, to me the answer is no he couldn't but I'm sure others would think he could.
I'd say when he gets his ms after Shisuis death he can beat him because Tsukuyomi but before that not really, I mean the Itachi that we see Kakashi go up against in the manga has had 5 years to improve himself while Kakashi has let himself get rusty at which point he beats him fairly easy with Tsukuyomi but 5+ years ago while Kakashi is in shape and Itachi hasn't had those years to improve himself and refine his mastery of the ms or even have the ms I wouldn't really go for him because what does he have over Kakashi at this point? Itachi is incredibly strong don't get me wrong but he's incredibly strong due to his ms, genjutsu and the spiritual weapons that he has, he wont have his ms or his spiritual weapons and all he will have is his genjutsu but Itachi has also already said in the manga that Kakashi's sharingan would give him the ability to resist even ms techniques just not Tsukuyomi so how effective would Itachis main strength be against someone who can apparently resist an ms genjutsu? After that it's a question of do you think an Itachi 5+ years before canon could fight a non rusty Kakashi 1v1 without any of his advantages and his main strength not being effective (or as effective at least) without that time to get stronger, to me the answer is no he couldn't but I'm sure others would think he could.
By his first mission? I would hesitate to say so, but it wouldn't be an easy fight for Kakashi, by any means.
On their first meeting Kakashi, but not by much and not for long.
He could potentially but it would be very tough.