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Yes, a 2MP image will be more jagged than, for example, an 18MP image when both are viewed in full resolution at the same output size.
However, an 18MP image downsampled to display at 1080p video resolution will be exactly the same as a native 1080p image, which is what this video-specific sensor probably has, so it won't be more jagged in that use.
Not necessarily. With the native 1080p sensor, you're basically stuck with whatever tradeoff between aliasing and blurry edges is built in to the hardware (as a function of microlens design, AA filter, etc.); depending on what Canon chooses, it could be jagged or smooth. When downsampling from a higher resolution image, you have the flexibility to dial in exactly the level of anti-aliasing you want, which might vary significantly between scenes (or even portions of the same scene).