The problem is not just living in Denmark because of coaches, but even if they marry there is no guarantee they can live in Denmark. To obtain residency for a spouse, they couple has to show that their 'combined total connection to Denmark' is greater than that to any other country. This makes it extremely hard for Danes who meet their spouses abroad to move to Denmark.
She might be able to get a separate residency based on her own skills, and they might be able to claim attachment by having represented Denmark, but I will not count on it.
I don't think they asked for a citizenship fast track - they asked the IOC for an exemption.
They probably knew she wouldn't get that. Remember that Wilson Kipketer in (EDIT) 1996, was pretty much a guaranteed gold medal in 800m, and he was training in Denmark, had attended university in Denmark and lived there many years with his Danish wife. He didn't get fast tracked.