The path to the olympics is open to anyone, from any organization. the style of sparring in the olympics is set by the WTF, so there is no way for example to fight point style in the olympics, but it doesnt matter if you are a karate practitioner, if you want to, you can fight your way up to the Olympic Trials.
USA Taekwondo is responsible for choosing the US Team, they are appointed as the National governing body for Taekwondo in the US. In order to compete at USAT events you have to:
1. Become a member of USAT ($35/annual)
2. Fight in a state or regional USAT event, place in the top 4
3. Attend nationals. fight in the "World Class" division. (only open to those that qualified at a state or regional event).
4. Place in the top 4 - attend various team trial events to make the US Team.
National teams are selected only for 14 - 17 year old black belts and adult (senior) division. No color belts, Ultra, or 13 and under teams at this time.
As far as organizations coming together - It depends...the WTF is the sport organization for Olympic TKD - if they can grow, the sport grows, which is good for everyone. But independent organizations will always exist. IF you look at the history or TKD - its pretty obvious that people can't seem to get along, how many splits or organizations are out there...its as bad as religion! ;-)