Our 2010 Prius was stored for the winter with a battery maintainer on the 12 volt battery. When the car was started, the engine fired up but made a terrible racket as it stumbled and vibrated, flexing the motor mounts. Within a few seconds it was smooth and quiet. The drive battery charge monitor looked as the same as when I parked the car (two lines from the top). The next couple times the engine was started, it stumbled for a second or so, but now is smooth and quiet as usual.
I don't own a 2010 but I have herd a lot about the 1.8 running rough sometimes during a cold start or after sitting a while. There is videos on YouTube of it. I haven't herd of any damage coming about it.
Wrong forum but yes, goto the Gen 3 maintenance section and you'll see the TSB stickied at the top of the forum. The engine was coughing out the moisture that had entered by way of the defective intake manifold (which the TSB addresses). YMMV in getting your dealer to fix it. I got sick of fighting it and "traded up" to a c. :x