Possible to assign Smart Groups’ Search in field from template?

Is there any way to export (save to Templates folder) Smart Groups – as part of of project template – in such a way that one can assign Smart Groups’ Search in field to refer to the project project Group (or any other designation, apart from the default “Database” setting)?

As far as I know, template-produced Smart Groups’ Search in is set to “Database” automatically, and there’s no way to change that while assembling a template. Just wanted to be sure that’s true.

Thanks!