Did someone say castrati??

By role, do you mean like what parts they played in operas?

I don't believe there's any link between castrati and the Ospedali in Venice to speak of. Putti castrati (little boy castrati) were trained stereotypically at the 4 conservatories in Naples, though other places too. I don't know offhand of any adult castrati who worked at the Ospedali della Pieta, though it's certainly possible some did. Nobody "big" worked there for sure. If you're thinking that they'd try to hire mostly castrati to teach to help preserve the "purity" of the girls, nope. Also (recalling some very overview level knowledge of this conservatory) it focused a lot on instrumental training, right? The castrati were typically only skilled in keyboard work (though many were very skilled at that), so if you were hunting for a violinist virtuoso who happened to also be a castrato, you'd have a bit of a rough go of it! (Though I know of a few castrati who were instrumentalists more than singers.)