I'm kind of guessing here....
Assumption: The artwork in illustrator contains various opacities and blend modes. This makes the object appear a certain way on the artboard(s). But when copied to the clipboard any varying opacities/blend modes get lost.
So, I'm guessing what you are seeking is a method of flattening artwork on-the-fly when it is copied to the clipboard. So that what's on the clipboard looks the same as it does in Illustrator.
If that is indeed what you are asking....
Then no. There is no method to flatten on-the-fly when copying objects to the clipboard in Illustrator. Objects would need to be flattened directly before they are copied to the clipboard.