The secondary air needs to be heated, so it does draw internal air (minimal) and the Doghouse air is internal (preheated) and also very minimal? The Primary air is where majority of your air comes from (even when closed COMPLETELY it doesn't shut 100%) and being an EPA stove they are designed to always let some air in (not to smother).
Mike commented on a thread not to long ago that spoke to OAK's (Englanders of course) and stated that the Primary draws more than secondary and doghouse).
If you look inside the Primary and open and close the lever, you will see how big of an opening is left. Even when shut down 100%.
An OAK will always help the efficiency of a stove. Using inside (warm air you already used BTU's to heat) air for 100% of your combustion and sucking all that air in through the door sills, windows, and any other leaky points of your house? Or use an OAK and draw 70% from outside and keep that Warm air you already heated inside the house?? Which in turn, keeps the windows in your room from drawing cold air in, thereby keeping the bedrooms warmer.
OAK it. Especially if newer than 10 yrs. Your house is already pretty efficient being that new. Why not help it along?