Yes unfortunately it will overwrite. Application save data is stored inside the app itself so any time you remove/replace and app, all the data goes with it. There is a process described here using a $30 app that allows you to manually save and transfer data:
I get the whole sandbox idea and hiding the filesystem but at the very least, they can selectively keep a duplicate of save data in a safe place outside the app so that if you do need to delete/restore, you can just get all the data back again. Even if it said when you delete an app, 'do you want to keep the data' and if you hit yes, it will move the data to another location and list it somewhere like in settings. When you reinstall an app, you'd be able to restore it.