No because by that time Itachi's head is in Kamui world or he is coughing his life out due to trying to use Tsukuyomi again.You need to understand what counter is.
A counter to Tsukuyomi is basically immunity, such as Sasuke.
A check just avoids total damage, what Kakashi did was a check. If Kakashi was hit by Tsukuyomi again, the results would have been the same.