A travel system is really three products in one, splitting it into the car seat, base, and stroller before packing makes every piece lighter and easier to protect.
Pro tip: Pack the three pieces, seat, base, and stroller, as three clearly labeled units rather than one combined system, it genuinely speeds up both packing and unpacking.
Watch out: Keep the car seat and its base matched and clearly labeled, an unlabeled base among moving boxes is a common way to end up guessing at reinstallation.