A few years before I was born my aunt placed a baby girl for adoption. About a year ago, she wrote a letter to my aunt explaining who she was and that she would really like to meet her. She and her husband flew halfway across the country to meet my aunt, her husband and their children. Their reunion was one of the happy ones.
I have seen pictures of my biological cousin (who I have still yet to meet) with my aunt and with my cousins. It is so clear in the pictures that my aunt and my biological cousin are very, very happy to have had the chance to meet and to get to know one another.
She is facebook friends with my cousins (her half brothers and sister), so I sent her a message on facebook and we are now facebook friends. I don't really know her, and she doesn't really know me. But we both hope to meet someday.
I'm not really sure what kind of expectations she had when she reached out to my aunt. I can only guess at what questions she had about her past or curiosities in want to know more about her biological mother. I do know that in her letter she thanked my aunt for giving her life and for placing her for adoption, as she was placed with a wonderful family.
You said, "My parents who raised me are my parents," and I cannot imagine you would feel any differently. These are the parents who took care of you and loved you. They fed you at 3:00 in the morning when you were a baby and stayed up with you when you had the stomach flu. It is unimaginable that you would feel differently.
If you are interested in getting to know your biological grandmother, then it seems like you have a great opportunity to do that. Why not meet her for lunch. If you don't want to do this alone, perhaps your husband or one of your girlfriends would go with you? Just lunch, for now, and see how it goes. Take some time to just get to know her, as a person. You might decide that it was nice to meet her, but you are ok with the your life as it is. You could also get to know her and decide that this is someone you'd like to get to know better.
I hope this doesn't sound stupid but, it's kind of like dating. You just have to take a chance and meet with her. You can have all the expectations in the world. She can have all the expectations in the world. But neither one of you is going to know until you try. So if you're up for it go ahead and meet with her and just see how it goes.