I have never had dreams about a poly relationship, but I have had some pretty wild dreams in my time, such as dreams about places I would move to (Albuquerque, Seattle), and I actually ended up moving there.
I'm kinda confused at what you're getting at here. Are you talking about crushing on someone and wanting to live happily ever after with them and the rest of your polycule? Are you fantasizing about orgies? Are you wanting to grow your polycule by dating a new person yourself (and only you)? What do you actually mean by "becoming a part of your poly relationship" because there are so many ways of doing poly relationships.
Here's an old thread about fantasies and dreams of living a poly life, while being stuck in a mono marriage in a conservative area of the deep US South. I don't know if you can relate.