Good Lord! This is where I wish my Grandmother had been more open minded like you! Strict Roman Catholic, very Southern Baptist on the other side.
You know, I don’t know the details like: does she need a place to live, are they not able to support themselves; or, is it just a starting point for the couple? I guess though, it really doesn’t matter, you seem to be okay with it, and that is what matters.
I do agree with @jca, there could be problems and sooner, rather than later. Your grandson is used to you, your family and how things go in your house. The girlfriend isn’t and may not always agree with things. Putting your grandson in the middle.
I just get this gut feeling that it isn’t the best idea. Sorry, no source except my own gut.