There are plenty of paved roads. You can check the Biking Across Kansas web page (especially the archives) to find lots of maps:
http://www.bak.org/index.php
The paved roads will be busy.
If you go west across the state, you'll almost certainly be dealing with a steady headwind.
Kansas has loads of dirt and gravel roads. The condition varies tremendously. In the northeast part of the state, they seem to be fairly reliable (i.e. they match existing maps and bridges are in place). I've heard that they become less reliable as you get to the middle and west part of the state.