Can DoT inflict poison with the boots Beacon of Madness?

These are the newest Unique boots introduced in 3.10, Delirium League:

I'm wondering if the mod "Damage inflicts Poison while affected by Glorious Madness" will allow for the Chaos DoT that Caustic Arrow creates to also inflict poison. As far as I know, Caustic Arrow does not poison on hit, nor does its Chaos DoT innately poison on hit. According to the DoT Gamepedia page, both the modifiers of "Damage" and "Damage Over Time" will apply to Damage over Time scaling. Now I know some modifiers have specifically designated applications, such as "Damage with Hits" and "Damage with Ailments", both of which do not refer to Caustic Arrow's caustic pools. But the wording here specifies "Damage" specifically without any other modifier.

Can DoT inflict poison with the boots Beacon of Madness?

Poison requires a hit to be applied. Since DoTs do not hit, they can't poison. Caustic arrow does however hit enemies, in addition to the caustic ground it creates, and that hit can poison.