You cannot have linked images in a PDF (well, technically, the PDF spec allows it, but Adobe products won't generate this variation of PDF).
Among the reasons:
a) With a linked image the document is no longer portable (the 'P' in PDF)
b) With a linked image, you cannot reliably sign a PDF, since the referenced image could change
The linking/embedding option you see in Designer applies to whether the image is embedded in the template.
When the PDF is generated from the template, any linked images will be added to the PDF.