I have been in a number of dojos over the years and it has been my experience that it isn't when the relationship is "on" that you have a problem. In fact quite the opposite. When two people are in a relationship and can share their training you are quite a bit more likely to see them in class frequently and they are apt to participate in the life of the dojo more than those with significant others who don't train.
But the big risk is if the relationship doesn't work out. I have seen a number of romances and several marriages go by the wayside within the dojos where I have trained. In every instance it meant that the dojo lost a student.
So I am always of two minds about couples and students who have relationships. It usually is at least nice while it lasts...