Bitters can be a detail meant for aesthetic flourish in an egg-white cocktail À la latte art, or they can be a vital part of a cocktail's build, like in an Old Fashioned.
You can be assured for the most part though that if you see a bitters ingredient listed in a cocktail, you will taste it.
As the name implies, bitters are super dense in flavor, and usually high in alcohol by volume. You only need a drop or two for impact.
More than once I've kicked myself for forgetting a drop of bitter that changes the entire character of a cocktail. On my current menu, I work with a cocktail called The Diablo that can be served with or without a locally made ghost-pepper bitter.
Even though it's only one drop, it's been sent back multiple times on account of being too spicy.