Not really. I've got these trolls named Wayne, Bill, Chuck and Roy that I harbor inside my quiver of board bags. They each have one bag they call a home. After a sesh, I take my soaked surf stick and shove it in the bag. At that point, my trolls take their chamois and dry the schitt out of those boards.
So, to be technical, no, I do not dry off my board before putting it in my bag. But as soon as that foam hits its sheath, those trolls are shining it up proper with their wash leathers.