Even ignoring the fact that the megapixel count doesn't necessarily mean that's how high your video resolution would be since the processor can only handle so much, no, 13 MP would not be enough for "6K" video.
If we go by 2K being 1080x1920 and 4K being double that at 2160x3840, 6K would be at least triple 2K at 3240x5760 which would require a minimum of 18.7 MP. 8K would require at least 33.2MP.