The game is supposed to use the ships we've designed against us... but I've only ever seen a few of my more basic designs because the AI NEVER chooses the "minimization" path and I almost always do.
They do sometimes for me (rarely), but even if they did, cost is another factor that will make it almost impossible to effectively copy your ships, at least relevant ones. Fully loaded ships with reduced mass components are usually too expensive for a shipyard sponsored by only one poorly laid out planet. It would take several dozen weeks to make just one given AI capabilities, which is going to hurt them more than help.
Not that the AI can ever copy my endgame ships powered by level 20+ Hyperion Shrinkers. lol They would be lucky to have any improvements break level 5.