My TM pro goggles also draw the air out of the top rather than blowing air into the mask.
I steamed mine up in the first 5 minutes of putting them on, (at the chrono station, hadn't even made the game zone), but the fan did a good job of defogging me. The batteries lasted all day easily too. Being used only when they were needed, which turned out to be quite a lot, and as the day wore on, I left the fan running longer and longer with no sign the batteries were about to give up.
This was in indoor CQB site and I haven't used them in woodland yet but I'm expecting them to fog less due to