No, not an advantage in the game sense. It just tells you how much you can carry, or lift, or drag. It does give you and advantageis advantageous (but not "advantage"without giving you advantage) onfor picking things up, in that it tells you how much you can pick up, so a higher carrying capacity means you can pick up a bigger thingheavier things.
It's linked to the other stuff, in a way, since carrying capacity is a function of strength, and those other functions generally involve strength rolls, but that's already built into the strength rolls.
Your carrying capacity can also be affected by your size, or by having a "powerful build"powerful build (such as goliaths), and that just modifies how much you can carry/lift/drag, and not much else.