Hi Sandi. I have grown turmeric directly from the rhizomes that I bought directly from a local green grocer. So my experience is - yes, you can. However, I have heard that some growers treat them to prevent growth occurring while in the store. Therefore, I would recommend getting your turmeric rhizomes from a quality organic grower or health food shop.
Good luck :)
Some good advice Graeme. Thanks for sharing your experience.