Is it a legal play for a player to "save the ball for him or herself?" In other words a player saves a ball from going OB, the player goes OB and immediately returns to the court, and is the first person to secure control of the "saved ball." It is legal under NF rules(Case Book Play 7.1.1c) but how about NCAA rules?

Yes, legal as long as there was no player control.

If he touches the ball before restablishing position inbounds that would also be a violation.