I think if you decline the fix then you could potentially void any remaing warranty (at least regarding the engine and anything emissions-related). Supposedly the non-fixed cars will also be harder to sell (because at some point VW/Audi will stop fixing them for free), and also you kinda sorta maybe breach some emissions regulations without the fix. The more important question is whether you can actually get in trouble for it.
On the other hand, my car runs perfectly fine and the engine feels responsive across a large rpm range while the fuel consumption is also reasonably good. And now Audi is supposed to fix that emissions-problem without touching any of the other parameters, and with just an updated software? So either the software really only disables the cheat that tells external devices wrong emissions values, or it adjusts some of the properties of the engine and makes it cleaner, but overall worse. (Because if it was possible to have the engine this good and also clean, then why cheat in the first place?)
In case they actually change something about the engine I expect either the power to go down (which would be annoying) or the fuel consumption to go up (which wouldn't be too bad).