What would happen if Napoleon annexed the Confederation of the Rhine?

You have the freedom to choose when, just be sure to elaborate on the consequences you envision and not get bogged down in the question of Plausibility.
Several million Germans would go from being more-or-less willing allies of Nap, to resenting the hell out of losing what autonomy they had as client states. It would be a large and restive population that could only be integrated into the administration of the Empire with great difficulty. Plus, Nap would lose his eastern buffer for the Empire "proper" and have potentially-hostile Austria and Prussia as neighbors along the entire eastern frontier. The people would begin to see the Austrians and Prussians as potential liberators... Political alliances could turn on a dime in those days...
Alternately, he could unite it all and establish a "Kingdom of the Rhine", and assign it to one of his relatives, marshals, or close allies ("Kingdom of Rhenish Saxony" perhaps?), but that sometimes didn't go too well either - think Spain. I think central Germany was just too fractious at this time to make this workable.
To sum, he would have few good reasons to do this, and plenty of good reasons not to... which sometimes didn't stop him in his decision-making process :)
Imagine all the new departements that would come from this 🤤

But yeah probably not a good idea, and unrest may spread to the left bank of the rhine
Quite apart from the French Revolution, mediatisation of smaller principalities, especially the ecclesiastical ones had been a long term goal of the larger princes for ages, so they agreed to the confederation because it wasn't necessarily France going in and telling them what to do, it's France going and creating the situation needed to let them do what they wanted to do anyway. If France attempted full annexation, this would not have gone down nearly as well. Perhaps instead of confederation, you could have Napoleon be crowned Holy Roman Emperor which would make him the direct overlord of all Germany but it also means he'd have to respect imperial bodies such as the Reichstag and Kreis associations.
All depends which German states are restored in 1814.

Hanover certainly will be, as its ruler also rules a great power, and Oldenburg is also a sure bet, as the Tsar is a member of its ruling House . Beyond that it's anybody's guess. Does Prussia get Saxony and Austria get Bavaria?