Sort of. They had a system where a single lever would release bombs, then level and recover. Their system would not engage after the pilot passed out, rather engaging the system would make the pilot pass out. This allowed them to "safely" dive bomb at 90-degree angle, making them much more accurate than any other dive bomber from the period.

The downsides were that the automatic recovery was very-high-g, almost guaranteed to make the pilot pass out, and flying slowly with the pilot passed out in a very predictable pattern over enemy troops was not very good for you, especially after the enemies figured out the recovery pattern.

Interestingly, according to this source some german pilots disabled the Stukas automatic dive brakes (pull-up mechanism) since the flight profile from an automatic recovery would be very predictable for ground troops trying to hit you.

https://www.warhistoryonline.com/war-articles/ju-87-diving-p...

Edit: It would be engaged after dropping bombs; not when the pilot was unconscious.