Jim I think you do whatever is comfortable to you as long as you can do it with no emotions, no expectations and it doesn't have an impact on your children giving them the impression that mom and dad are getting back together.
I would say it does seem kind of odd but every R is different and has their nuances. My EW will invite me but she has not invited herself.
I would also say that when you start to date and get serious with another woman I highly doubt you will feel comfortable with this happening and then you will probably say "no" if she asks.