Hi Enlightningbug,
When you import an image (Insert > Image > From File...), the image IS a Visio shape, and the text is at the bottom, but as you've probably noticed, it's a brand-new shape. So if you've done any tweaking to a shape, you can't re-use this without some work.
The built-in Visio Org-chart solution allows you to insert pictures into each position-shape. You might be able to utilize that to some extent.
To do this with your own shapes, however, would require a bit of code.
It's something I'd like to publish in a utility packet one of these days...but I wouldn't be surprised if someone else offers some sort of tool already. Check out the
Visio Guy Visio-links page