According to Washi's blog post from 2011 titled "Anime Production – Detailed Guide to How Anime is Made and the Talent Behind it!", all of the voice work and sound recording happens in post production. These processes are compiled from studios like Sunrise, Production I.G., AIC, etc.
I've read about certain productions where some animatics (simplified mock-up animation of storyboards) are used with voice acting. Not sure if they actually do recording there or whether it's used as part of the creative process. However, Wikipedia's Voice Acting in Japan notes that:
A voice actor's role in anime consists of reading the lines before the production is finished. In Japan, the lines are usually performed before the anime has completed. The artist then draws in every expression to the key of the voice actors reading it off. This is the most common way of prerecording in Japan.
But the passage lacks any citation.
Additionally, voice actors are paid for a chunk of work, regardless of the number of lines or how long the session takes, so it's logistically easier to do it all in one go as opposed to being linked closer to the production of the actual animation. When the animation is (mostly) done, the voice acting and sound engineering can all be done in one go.