In summary, not a hope in hell.
AYRE (Ayers Rock Airport) to Ayers Rock is about 20KMS
A Rwy 31 arrival to AYRE would give you views out of the port side.
Alice Springs is about 350kms ENE from YBRE,so I doubt you will get a view, unless you were arriving from Perth for a RWY 12 arrival.
You can see the airport charts
Here