Not familiar with the dates of the differing programs - but yes, you don’t wait. If a program opens later, get in, then apply when it opens.
Many schools - in the SE anyway - you apply and deposit housing before acceptance or you get a bad spot.
The app is here - you can email and ask the timing - like should you wait til your into the university or should you apply to Honors too - they’ll answer you.
murrie.j.dixon@ua.edu
Apply – The Blount Scholars Program (ua.edu)
Edit - I just read what @laceltris wrote - follow that!! But never hurts to email if have questions - or rather have the student do so.
Good luck.