Hiya Eric,
If you're talking about access to a specific product alone then that would probably be no... unless (and I could be wrong here) you were to setup the shop and not make any changes at all to the ordering of the products in that category, nothing turned on and off etc for whether it's published or not. Then you "might" be able to get away with it by using the specific URL for that product and setting access rights to it. That would "I believe" be like restricting access to a page for the most part which in the end is what you would be doing.
I am not positive how changing orders, and publishing and unpublishing a product affects the URL which is why I mention it. You could play around to test that theory also as maybe the URL is always the same even if you unpublish and then republish it. Dunno, never ventured to need that info.
If this works (being that I don't know how access around the products might affect other things), then you wouldn't have to setup any certain shops for specific products, you could theoretically set this up for many clients to access different pages for payments etc. Just keep in mind that your users would always need to enter a password to access that page, there is no account based setup, only page/file/directory access itself and therefore no account info or login system is used. If you're clients don't care about that then this "should" theoretically work.