We would not need any "permission" or "approval" from ASU. Also ASU is already the largest university in the country and is struggling to meet the needs of the Phoenix metro area. That is one of the reasons that GCU, a private school, is thriving now.
Expecting a correlation between an AZ campus and improved sports recruiting to BYU is probably wishful thinking though, other than perhaps for a few AZ LDS athletes. Do we lose many of those currently?