No, you don't. To adopt kids without the bedroom wing, you need the two beds and dresser built in the upper level of the Main Hall. Your spouse can sleep on the large bed that you build on the other side of that floor. I'm surprised this bit of misinformation is still floating around after all this time.
Indeed, people need to know that none of the wings are "required" for anything, you can still adopt without the bedroom and you can still do alchemy and enchanting without the towers, all those things are also in the main hall. Customizing your wings are more for aesthetic reasons so don't feel like your forced to get any of them, choose the ones you want, not the ones you think you need.