What occurs to me about this question is a little bit of psychological wordplay... a lot of people have mentioned emotions and trust, more or less in the same sentence. A lot of lifestylers talk about respect as well. The impression I seem to get is that these three things are believed to be tied together, almost to the extent of being the same thing - you cannot have one without the other.
Is this really the case? I think it is worth analysing it in more detail....
Casual play. We've all done it. Even if it is only vanilla sex. Even if it is only 'going on a date with someone to see how it goes and never calling them back'. Sometimes thats all it is - a casual, one night stand. However, quite often, you go on a second date, have sex again, let them tie you up once more. This leads to a third date, a fourth... At what point does 'casual play' become a 'relationship'? Every relationship begins with a casual arrangement.
You could argue that a relationship starts when the emotions kick in, when you start to love and respect them. But can you accurately pinpoint when this occurs? I think for BDSM it may well happen a lot sooner than you may think because one thing BDSM is built on is trust and trust requires respect and some inkling of a relationship. Before you can trust someone enough to put your life in thier hands, you have to know them pretty darn well and that is a relationship - however slight it may seem on an emotional level.
And this is not limited to those in the lifestyle. I have a very good relationship with a Pro Mistress. Its not a sexual relationship (for all that she has explored a part of me no other woman has yet been...) nor is it anything romantic. However, I have what I would call a very good friendship with her - a relationship built on mutual respect and trust. I believe many of the repeat clients of some of the better Pro Dommes feel the same way about thier Mistress and many would not consider going to another because they would not have this relationship with her.
Something to think about and discuss in this topic, I think: How casual is casual play really?
As for the Poly issue, these relationships do need a lot of care and attention. I have several friends who are in the poly lifestyle and therefore often get descriptions of how they organise their lives and it is very structured and complicated. There are rules and boundaries which must be adhered to because crossing that line may well lead to jealousy and emotions and break ups. At the start of every poly relationship, or when a new member joins a relationship, it is necessary to sit down with all involved and discuss the rules and boundaries - the schedules of who does what with who and when. It also has to be recognised that everyone in the relationship has an equal emotional investment in it and therefore deserves equal time. You can even go so far as to draw up a timetable. This step can eliminate many problems.