OK, this works with external manual flash, at least. We did a family portrait this evening here at home. Even though I was using my standard 2 flash setup, with umbrellas, etc., I wanted the tree lights to show instead of being overpowered by the flash units.
I set up the shot as normal, using the 1/200th sync shutter speed and proper aperture to capture the right amount of flash. Once I was happy with the settings, I only changed the shutter speed to 1/10th second and warned my family to stay very still until after the flash had gone off (I was using the timed shutter and running into position).
Worked like a champ. Obviously, I was using Manual mode on the camera. Also, there were no other ambient lights on in the room (after I focused, then turned them off).
Realize that if your dogs move, it probably won't be noticeable, as the flash has performed 99% of the lighting for the subjects. You may get a little ghosting. If so, up the shutter speed a little faster and try again (assuming your lovely subjects will stay around long enough for you to experiment).