Does CDCl3 also Knock People Out?
In almost all respects, deuterium behaves like hydrogen, chemically. You can safely drink pure $\ce{D2O}$ in reasonable quantities (though not enough to replace more than ~25% of the $\ce{H2O}$ of the body). In fact, prokaryotes can continue to grow in ~100% deuterated media, albeit more slowly. It does prevent mitosis in eukaryotes in large quantities, though.

Given that similarity, there is no reason to assume any different behavior between deuterated chloroform and that with just protium. But don't knock yourself out trying the experiment, as chloroform is hepatotoxic.