I can't imagine they can really keep up with the large fanbase schools
Tradition and reputation are very powerful recruiting tools in the "old world." In the "new world" I suspect that money will be more important. In the NFL, NBA, MLB and pro Soccer (globally) the amount of money you pay a player seems to be the largest determinant of landing high quality players.
So, the question is whether KU (relatively small university) and a collection of alumni from a very, very, very small population state in the middle of the country will have enough money to complete with schools with enrollments, state populations, and donor lists twice their size (or more) in the New World.
After Bill Self moves on, will the next crop of coaches look at Kansas the same way that Bill Self looked at Kansas?