Welcome to the forum. I would say it really depends on your dog. If it is a breed that is hyper most of the time & barks at everything, it could stress it out. Since they will be in separate rooms when you are not home, I would think neither the dog or the parrotlet would be too concerned with each other. And tho I have never owned a parrotlet, I have had a love bird and they are not super loud when vocalizing.
I have dogs & I have 2 macaws, an Eclectus, a conure and 8 budgies. My dogs (poodles & shis tzus) do not pay my birds one bit of attention when my flock gets to rocking & belts out their rendition of the rainforest medley. And we all live in the same big room together. On the same note, my flock doesn't pay the dogs any attention either.