Hi,
As you might know, both of our template and the Virtuemart itself are open-sources.
So every kind of modification is possible, but of course with custom coding.
Currently within our template, the "Sold Out" badge only possible to show on the category browse page. On the product details page, the "add to cart" buttons turns out to be "Notify Me" button if the product is out of stock.
With custom coding changes, it is possible to put SOLD OUT badge in the product details page as well.
Unfortunately custom modification and custom coding is beyond our free support.
You would need to purchase "premium support" through here:
www.flexiblewebdesign.com/Premium-Support/Virtuemart-Premium-Support (1 hour is enough for this modification)
and let us take care this modification for you.
Regards.
Support & Development