Is the intent to be able to follow links if the user does not have Visio? If so, I'd say can't be done. Embedded files must have access to source app.
I tried saving a Visio file as a PDF, which did allow the link to remain live and I could follow the link from within Acrobat. But when I embedded the PDF in Word, it came through as a static image. And I have Acrobat Pro, so if it were possible for a PDF to remain live, that would have worked.
Alternative: Save Visio diagrams as PDF files, keeping the default options (dialog box appears). Save Word doc as PDF. Combine the two in Acrobat Pro or one of the free/cheap online PDF building tools.