Yes—in fact, translating Shakespeare into biblical Hebrew was the default approach in the early days of Hebrew theatre (end of 19th, early 20th century)—since Shakespeare’s English is roughly the contemporary of that of King James translation of the Hebrew Bible.
Shaul Tchernikhovsky (a well-known Hebrew poet and author, who also translated) was a fervent adherent of this approach. As Nurit Yaari (a professor of Israeli theatre at Tel-Aviv University) points out in her forthcoming book, Between Jerusalem and Athens, Tchernikhovsky believed that all classic plays (of ancient Greece and Rome, as well as Shakespeare) should be cast in biblical Hebrew. But in 1947, the actors of the leading Hebrew theatre, Habima—
soon found that they had to make many revisions to Tchernikhovsky’s text to create a performance text that they could fluently declaim, and which the spectators could readily understand at first hearing. Since Tchernikhovsky was no longer alive, they turned to one of the leading poets of the new generation, Avraham Shlonsky—a young innovator of the modern Hebrew language and Hebrew poetry modernist—to convert Tchernikhovsky’s biblical prose into theatrical text.
But within twenty years, attitudes changed. In Arie Sachs’ 1968 production of Aristophanes (admittedly, not by Shakespeare, but Euripides), the language used was a mélange of biblical, medieval and modern Israeli Hebrew expressions, resulting in a doubling or tripling of the worlds.
The result (in my simulation of Sachs’ Hebrew) is like this:
The beetle shall be my chariot. And when I bring Peace, the lowly will be raised on high, the crooked shall be made straight, the rank will smell of roses, nard, and saffron[…] Ho, people of Athens, for ye I risk my life! The finest for the Air!
‘My bowels, my bowels! I am pained at my very heart; my heart maketh a noise in me; how can I hold my peace?’ (Jer. 4:19); ‘Wilt thou forsake me?’ (cf. ‘Forsake me not’ in Psalms, e.g. 27:9; 38:21, 71:9, 18; 119:8, 138:8); ‘Shalt thou prefer crows and flying storks over thine only daughter whom thou lovest?’ (like ‘Take now thy son, thine only son Isaac’—Gen. 22:2); ‘Woe is me that my eyes have seen this’; ‘Hear me, o God’ (as in ‘Hear me, o Lord’ in I Kings 18:37; Psalms 13:3, 30:10, 69:13, etc.). When Peace arises from the pit, Trygaeus said: ‘Who is this that riseth out of the pit like pillars of smoke, perfumed with myrrh and frankincense?’ (cf. Song of Songs 3:6, ‘Who is this that cometh out of the wilderness?’ etc.)—and Peace replies: ‘Dost thou not know me? I am Peace—as in “Peace Upon Ye,” “We come in peace!” “Peace and Welcome!”—and all that’…
Ten years later, translator Aharon Shabtai expressly abandoned the biblical Hebrew approach altogether, explaining:
Previous translations […] saw [tragedy] as something classical and sublime. All these translations belong, in terms of their approach, to the nineteenth century, which ended with Ezra Pound and T. S. Eliot. These are translations that see literature as an arithmetic essay of beautiful words of a static nature: each word is worth such-and-such in its own right, like a gem.[…] In my case, words have a dynamic value: their value is a product of their context. Beautiful words are a myth […] My translation is the post-Modernist revolution […]
Today, Shakespeare is definitely not translated into biblical Hebrew any more. Pointing out that in Shakespeare wrote his plays in a language that the common people understood, modern translator David Parnas is currently engaged in casting all of Shakespeare’s writings into contemporary, colloquial Hebrew (and placing it in the public domain, on his website, שייקספיר ושות [Shakespeare & Co.].