Hi,
That video is certainly suing After Effects for the graphics. The voiceover can be done before or after it doesn't really matter, the editor would read through a script as they edit for the timing and whoever voices over will be roughly the same, adjustments can be made either way. i am able to animate graphics like this easily and efficiently, it just depends on the volume of work to be animated. If its more text that would be quick than if various objects have to be created before being animated. If you have further information about what needs doing I can give you a better insight into cost/time.
Thanks,
Jeremy