My own experience is about like many others have posted - I need some primary air and flame to keep things hot enough and keep enough gas coming from the wood to support secondary burn in my stove. However, you asked if a secondaries-only burning is the only way to have an efficient burn (or something to that effect). First I think we have to agree how to measure efficiency. I think an efficient burn means completely burning the wood, thereby getting the most heat possible and emitting as little burnable wood particles or gases as possible from the flue. I guess other definitions of efficiency include getting the most heat from the stove, using as little wood as possible to heat your house, and probably others.
Any time you have enough air to fully combust the wood you should achieve maximun efficiency. If that happens in a crazy firebox-filling inferno or if it happens at a slow rate shouldn't change the efficiency. With a really hot fire you probably have a chance of gases coming out of the wood too fast for the secondary air supply, not fully burning all the gases and losing efficiency. WIth a lower burn you have the chance that temperature in the firebox isn't hot enough to burn all the gases, or the gases are not concentrated snough to support combustion, so gases escape and you lose efficiency. However, it soulnds like with your stove you can set the primary air low and still have steady secondaries, so you are probably getting high efficiency. I think there are others ways you could get similar efficiency as well.
Any time you have enough air to fully combust the wood you should achieve maximun efficiency. If that happens in a crazy firebox-filling inferno or if it happens at a slow rate shouldn't change the efficiency. With a really hot fire you probably have a chance of gases coming out of the wood too fast for the secondary air supply, not fully burning all the gases and losing efficiency. WIth a lower burn you have the chance that temperature in the firebox isn't hot enough to burn all the gases, or the gases are not concentrated snough to support combustion, so gases escape and you lose efficiency. However, it soulnds like with your stove you can set the primary air low and still have steady secondaries, so you are probably getting high efficiency. I think there are others ways you could get similar efficiency as well.