Translating Shakespeare into biblical Hebrew was certainly 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.
In truly ancient Israel (i.e., before Roman times), emphatically no.
To quote from Nurit Yaari’s forthcoming book, Between ʻJerusalemʼ and ʻAthensʼ: Israeli theatre and the classical tradition* (Oxford University Press, in press):
Theatre, as an art, a community event and a cultural institution, is entirely ‘Athens’ in nature: that is where it was first created in the late sixth century BCE, and where it acquired its form, conventions and concepts. As a visual and performative art, it is rooted in all aspects of classical Greek art—poetry, music, dance, sculpture, painting and architecture; indeed, their fusion is what gave rise to this independent and unique art form. […]