Will noise be an issue when joining two rooms with a circulating fan?
This plan won't really work without a full circuit. You need exhaust and return, otherwise the return may be from somewhere undesirable (such as under the door or through leaks to the exterior). The fan will create low- and/or high-pressure regions and air will find a way.

I'd consider routing both through the attic or basement for sound attenuation, and look for internally-insulated ducting for further sound deadening. Openings in the wall will feel like windows with respect to sound and privacy.