Can renders be made to include glossy reflections, after baking on textures without glossy in Cycles? I have a large interior scene with a lot of complex lighting, and I'm trying to reduce render times in it as much as possible. It includes lots of point and area lights, and exterior light filtering between beams. So, I'm looking for a way to bake the diffuse lighting onto the textures of objects, but have the glossy reflections be calculated during rendering. Can that be done?

It has occurred to me that maybe this can be faked, by baking everything except glossy, creating copies of the objects, and under Cycles settings leaving only glossy on for the copies ... Would that then mean that rendering is only calculating those glossy reflections on the fly, and doing everything else with the textures, so it is still a lot faster?

This is the sort of situation I'm dealing with:
Blender 2.79. Under 'Render" (down at the bottom) there is a section marked "Bake". Within this section de-select "Glossy". This is different from your workflow you described, which is to fake it through the Object settings.