I am fairly certain the answer is no but I just wanted to confirm.
In the PHB p.20 dwarves have the feature:
Speed. Your base walking speed is 25 feel. Your speed is not reduced by wearing heavy armor.
Monks have a feature called Unarmored Movement that increases their movespeed while not wearing armor (PHB p.78)
Would the dwarf speed feature counteract the unarmored requirement for Monks Unarmored Movement?