It sounded awfully good to me when they sang Soft Kitty as a round. Do they sing irl ?

Well, Jim Parsons (Sheldon) has appeared in a production of "Guys and Dolls" according to IMDB. And "Guys and Dolls" is a musical so going by that I would say yes, he does sing. And according to Kaley's profile on IMDB she has performed in theater productions of "Annie" and "Fiddler on the Roof" both of which are musicals. So apparently she also sings.