It seems to me that the Bible is pretty much silent on the issue of relationships. Friendship is hardly mentioned. There are regulations for how parents and children should act towards each other, but not much about loving relationships. Marriage is mentioned but hardly anything of a romantic nature is expressed. (Except in the Song of Solomon, which seems to embarass most Christians and is usually ignored.)
Many people think that when something is mentioned in the Bible, it is because God approves of it. Very often, however, the Bible portrays its main characters as greatly flawed. The Bible is a collection of writings that are very much culturally based in the time they were written. The workings of the ancient Hebrew culture or the New Testament Greco-Roman culture are much in evidence in the Bible. If the Bible would have been written in our 21st century western culture, it would have a much different flavor altogether.
I think the principles brought forth in the Bible are of importance. To me the key principal is that God loves us and for some strange reason wants to be close to us. Flowing from that love is our love for each other. To me the best summation of marriage in the Bible is the statement, "Submit to one another".
My opinion is that the Bible is fairly silent on relationship issues not because they are unimportant, but because each person and each culture has a different way of looking at relationships. God has given us a picture of love and how it works in our lives. God has given us freedom to make our own choices. I think God loves the diversity he/she sees in humanity. What the relationships are is not so important; how we love others and what our motivations are is important.
So are same-sex relationships a part of God's plan? If they are based on a love for each other with selfishness cast aside, I am sure that God is overjoyed.
For I am convinced that neither life nor death...neither the present nor the future nor anything in all creation will be able to separate us from the love of God that is in Christ Jesus our Lord. Romans 8:38-39