I have exposed wooden beams on a clerestory ceiling and have not identified any specific deleterious effect.
More than anything else, I would chalk the potential effect of some diffraction up to those beams. Not enough to break up a slap echo or anything, but depending on their size, any wavelength shorter than the beams height will get bounced around by them.
just by that photo, I’d personally be more concerned about how the windows and fireplace will have to be dealt with for best SQ.