The descriptions of rage point towards it being at least noticeable
Throughout the Barbarian class descriptions there are explanations or references to rage including the following:
These barbarians, different as they might be, are defined by their rage: unbridled, unquenchable, and unthinking fury. More than a mere emotion, their anger is the ferocity of a cornered predator, the unrelenting assault of a storm, the churning turmoil of the sea.
[...] For every barbarian, rage is a power that fuels not just a battle frenzy but also uncanny reflexes, resilience, and feats of strength.
[...] Barbarians come alive in the chaos of combat. They can enter a berserk state where rage takes over, giving them superhuman strength and resilience.
[...] In battle, you fight with primal ferocity.
At least to me, these point towards it being a noticeable shift. A sudden great increase in reflexes, strength, and many other things, they also gain more damage on their attacks and resistance to Bludgeoning/Piercing/Slashing.
The fact that this is a primal, berserker state of sheer force would lead at me to conclude that it is indeed noticeable. The Barbarian has gone from their usual form to this figure of pure, well, rage.