A little advance planning goes a long way. With the various wikis documenting resources needed for upgrades it's not a stretch to stockpile the needed resources before acquiring a new building, then taking it from build to level 6 right away. Since it's a building I didn't used to have, not having it for 2 more weeks isn't any kind of hardship.
"Very little is needed to make a happy life; it is all within yourself, in your way of thinking." ~ Marcus Aurelius
^^^^^^^^^^This.
Concerning Elite Barracks, you can build it before you need it. Get it to level 6 before you use it. Problem solved. For regular barracks, just have to focus on other things while its going up.
reduced productivity would be reasonable yes