Do forged alloy crank arms suffer from age-related fatigue?

Aluminum has no fatigue limit and thus it is impossible to make an aluminum bike part that won't fail with enough use.

Fatigue accumulates with load, not time.

Good forged cranks with designs that avoid stress risers in the spider area tend to be pretty good at resisting fatigue failures more or less indefinitely in practice. Weight weenie designs and bad spider transitions do cause exceptions to this. Some riders are also just plain good at breaking cranks, i.e. by being strong and favoring a low cadence.

Heavily used 40 year old aluminum do cause you to make a decision about the risk. If they're lightly used, there is no cause for concern.