Can a Victorian parlour organ (which is a type of free-reed pump organ) have vibrato tones, or is vibrato only a feature of electric organs?

My sister once had a reed organ that had a supply of air to produce the music through the reeds—it sounded exactly like a Victorian parlour organ. A parlour organ is also nice for Christmas carols and the like. But I really like the vibrato effect of midcentury horror movies and soaps, which were produced on electric organs typically.

Can the vibrato effect, such as in Jumpin Gene Simmons’ song ‘Haunted House’—be produced on a pump or free reed organ? Or is it only a feature on electric organs?