Normalize makes all moves used by the Pokémon with this Ability act Normal-type instead of its ordinary typing.
All moves. Hidden Power is no exception; I don't see why it would be.
Because of this, a pure Normal-type Pokémon will never receive same-type attack bonus when using Hidden Power unless it also has Normalize as its Ability.
This is the only way a Normal Pokemon can receive STAB from HP. HP cannot be Normal type except for the Normalise ability, despite it being classed as Normal type in game.