From inspecting the code, it seems like the answer to the question in the title is "No". If that's the case, why doesn't the specials table simply use the associated products_id as its primary key?

I ask because a client has, over the past year, run into non-reproducible conditions where adding a special price (via products price manager) winds up adding the special twice ... resulting in the product being displayed twice on various storefront listings.

If each product can have only one special, I was going to simply modify the specials.php handling for the insert action to remove any previous record prior to the insert. If multiple specials are allowable, the solution gets a bit more tricky.