Yes, but you'd have to implement that yourself. Saving/loading the game is handled in the SaveGameHandler class, you can hook in there and call your script.
Please consider rating/reviewing my products on the Asset Store (hopefully positively), as that helps tremendously with getting found. If you're enjoying my products, updates and support, please consider supporting me on patreon.com!
If you're enjoying my products, updates and support, please consider supporting me on patreon.com!
I use SaveGameHandler class from OrkFramework to save the game when each scene load and run my other script.