Well, depending on your empire's tech level, Precursors and Swarm and even Invaders can be way less advanced or strong than the player. They generally don't scale with you.
But -- unless such a race included some weird new tech or other systems -- what you are describing IS an NPR. Or bog standard precursors, depending on whether or not they have populations.
Any NPR or spoiler that gets activated, stays activated, and expands or explores or exploits or exterminates according to its programmed behaviour. Start a game with an NPR and have that NPR stumble into the Swarm the first month, and by the time your empire finds the Swarm it will have harvested fifty systems.