So far, I've had only one time I couldn't play for a few hours (TF release.) other than that I've never had a problem.
I, like another poster has already said, have never experienced all these ads either. Usually if there is an add it's to a videogame. The add isn't intrusive either, it's usually something about Destiny or another game that takes up one of the little boxes.
I had an issue yesterday for like 5 min but it came right back and had been working fine. This usually happens to me when they are updating the store or something. Im still able to play online but i wont be able to see my pins or access the market place. After some time passes everything is up again and like i said it doesn't take long to do. This is only on my xbox one btw.