Now, I am happily married to a woman with ZERO interest in Aikido, and she would frown mightily on my starting up a "Aiki-romance." However, it seems to me that if two people have a mature and healthy relationship off the mat, that they came remain so on the mat. I know a number of couples who happily practise together.
However, some people tend to unheathy relationships. If an student or instructor who had a reputation as a "swordsman" (or woman) used the dojo as a place to prowl for conquests then no good would become of it. (I have heard plenty of stories about what meat markets gyms can be - I'll stick with Aikido)
PS My wife braggs to her friends about visiting the dojo and seeing me called out for the most "robust" ukemi of the night (a fine dojo tradition)