Cost reductions apply to whatever cost you would pay to cast a spell, whether it's the mana cost or an alternate cost.
The formula for determining the payable cost of a spell is:
Cost = [mana cost OR alternate cost] + [additional costs AND cost increases] - [cost reductions]
August 17, 2017 9:54 p.m.
Dash's reminder text states "you may cast this card for its dash cost." Since you are casting it in this manner, any additional costs and cost reductions apply.
So yes, it will work.