Well, sort of. According to reports coming in from Germany, Audi is preparing to launch a version of the A1 with a rolling cloth roof panel. If the intel proves accurate, the open-air version would stop one step short of the pseudo-convertible Fiat 500C, in that the aperture would essentially be a giant fabric sunroof, but not roll down the back.
The measure would undoubtedly save Audi significant development costs, but also keep chassis rigidity in check without the need for significant additional structural bracing. Either way, we're not looking at getting any version of the A1 on this side of the Atlantic any time soon, so as far as American buyers are concerned, this is all rather academic.