From my very limited experience, you don’t have to know how to actually build furniture, but you do need to know how it’s built. The product development cycle is way too fast to construct more than small models (for instance, a corner detail or molding sample). I’m sure different companies handle it their own way, but you should know how to hit a desired market, what styles are hot, how to detail with considerable finesse, including structure, jointery, assembly hardware, and blocking; and have a strong sense of sellable styling.
Knowing how to actually build furniture would be a great background, but not actually necessary. I feel the best designers have an inbuilt sense of the physical presence of the pieces they are drawing, and this generally comes from much experience seeing their drawings take shape, and living with the end product of their ideas.