yes, a copy will only go into the child theme folder if it is edited.
the other thing you are seeing has to do with the order that the field groups are added when the load point is added.
If the load point for the parent is added in a way that causes them to be loaded first then this field group will override the version in the child theme. You can sync them and save them but this will ultimately not have any effect. Any changes to the field group in the child theme will only be visible when editing the group and have no affect on the field group when editing content.
The condition I described happens when the parent theme json files are loaded after the child theme json files. This is what will normally happen.
The difference is cause by where in the array of load points the parent theme load point is added.
