Yes — it changes your Hour Pillar, which affects your inner world, children, legacy, and the hidden dynamics of your entire chart. The Hour Pillar can also determine whether your Day Master has a "root" — meaning whether your core energy is anchored or floating.
In practice, two people born on the same day but an hour apart can have entirely different output and career gods in the Hour Pillar, meaning their creative expression and legacy follow different patterns. An hour can shift a chart from balanced to struggling, or from ordinary to extraordinary.