Will aluminum continue to corrode after its surface is oxidized?
No. Aluminium stops corroding once a strong oxide layer is formed.

Aluminium is a fairly reactive metal. The reason why it usually survives in air and water under normal conditions is because the aluminium oxide layer on the surface is very strong and normally protects the metal from further attack. Even if the layer is disrupted, it reforms quickly preventing any further reaction. Aluminium oxide is a very strong compound and impervious to water and oxygen. In bulk form it is known as corundum and appears in nature as ruby and sapphire, just about the hardest non-diamond minerals.

But there are substances that can disrupt that layer and expose aluminium to attack from air and water. Mercury and its salts and gallium metal both do this. Once they penetrate the surface layer, aluminium will be destroyed fairly rapidly and will crumble to a weak bulky mess. See examples on youtube from NurdRage and NileRed.