I think having them meet early on is fine if that's what makes everyone comfortable and happy. A simple chat, coffee date, whatever, to make sure everyone's on the same page can be helpful.
But, I think it's inappropriate that your fiance wants it all to be a socially packaged deal. You should have alone time to develop relationships, and I don't think it's either necessary or helpful to have everyone joined at the hip from the beginning.
If, after saying hey or sharing a cup of coffee, they both hit it off and want to develop their own friendship or relationship, then yay for them! Unless you are specifically dating as a couple (which I'm skeptical about anyway), however, you deserve time to figure out your relationships in your own space.
Fly and I don't really meet each other's dates at all, except inadvertently. But we're weird like that