Back in HS, I was involved in a Dutch-language version of the Taming of the Shrew - translated a couple of characters and assisted with the production. The thing with plays is that any performance takes a different interpretation in any case, whether with or without altering the exact text, so the performances in translation are merely a little further removed. In the case of my HS play, the fact that the performance was in drag (boys in the main female roles, girls in the male roles) probably set it apart more than the language that was spoken.

But it depends on the play, no doubt, some are more verbal than others. Poetry is generally almost entirely verbal, so while you could make a great translation of a poem, it will almost inevitably be so different as to be almost a new poem entirely.