ADT is designed as a hiking trail but it can be an excellent dirt road/back road bike route in the East where it follows off-the-beaten track roads. You'd need good maps plus their route guide as it has many, many twists and turns. In the West, the ADT traverses national forests on trails which would be pretty tough on a loaded bike - plus would be illegal thru wildernesses.
I've been on stretches such as in Nevada - extremely, extremely remote - and a bad idea unless you have mucho experience with such conditions. There are better ways to cross Kansas - either TransAm - or pick your own - plenty of dirt roads along the section lines.
It a good resource, but should be combined with others.