Yes, as soon as you research the tech to put drones automatically in your planets' orbit and you are at war enemy fleets show up to besiege those planets and do nothing else but shooting down those drones when they respawn. Sometimes the AI follows up with an invasion fleet, but most of the time not.
The AI ignores shipyards and starbases nearly entirely, at very rare occasions they shot down one of those, although shooting down undefended shipyards is quite easy (apart from the start of the game).
