No, because estas isn't just creating an equivalence between the subject and the object of this sentence.

"Estas skribinta" is a tense of skribi, not of esti, and is a verb formed of two parts: the auxiliary, estas, and the participle, skribinta. This is similar to continuous and perfect tenses in English: she is calling him; she had called him.

Close, but not the same meaning.

Li estas skribinta la dokumenton.
He has written the document.
We know the document was finished, but not when. Could be a second before the person said it, could be fifty years ago.

Li ĵus skribis la dokumenton.
He just wrote the document.
In this sentence, we know the document was finished in the recent past.

It's OK and more common.

Generally, -inta = completed; -anta = proceeding; -onta = not yet.

Li estas skribinta la dokumenton = "He has written the document".
Li estas skribanta la dokumenton = "He is writing the document".
Li estas skribonta la dokumenton = "He is going to write the document".

A good explanation is available here.