Will molded wood stop molding/rotting after its covered by aluminum to shield it from weather ?

Just to clarify mildew and rot are not the same and both will continue to a smaller extent after covering the wood with aluminum.

The removal of exposure to the elements doesn't stop the progression.Removing the moisture from getting TO the wood helps,but doesn't mean it will end 100%

If there is still sun hitting that aluminum it will cause moisture to form(in condensation),this is common on roofs.The reason behind using felt paper or ice and water shield behind metal valleys is the indicator.

In the many years I have done roof repairs I have yet to come across a roof where the metal hasn't left some signs of reaction to the base it was against.

If possible, replace the wood trim with PVC trim. Never rots. HD carries a good supply.