^^^ I think Kraig should have answered "Yes / No."
Single action/double action does not relate to chambering the next round. It relates to the hammer and trigger. I shoot 1911s, which are SA only. To chamber the FIRST round I have to rack the slide. After that, the movement of the slide ejects the empty case and loads (chambers) the next round. This is why pistols with slides and magazines are called "semi-automatic." The old term for them was "auto-loading." With this type of pistol, racking the slide also cocks the hammer, and pulling the trigger only drops the hammer (the "single" action).
If I take a SA/DA like an older S&W pistol, I still have to rack the slide to chamber the first round. But, if the hammer is down when the chamber is loaded, pulling the trigger first cocks the hammer, then releases the hammer (two actions, or "double action"). With the old S&Ws and other SA/DA pistols, firing the first shot leaves the hammer cocked, so all subsequent shots are SA.
In a double action only (DAO) pistol, you still have to rack the slide to chamber the first round. But ... racking the slide does not cock the hammer (or striker). Racking the slide loads the pistol, but it remains uncocked. Pulling the trigger first cocks the hammer (or striker), then releases the hammer (or striker) -- the two (double) actions. With this type of pistol, the movement of the slide does NOT cock the hammer or striker, so all subsequent shots are also double action.
Regardless of the action type, starting with an empty pistol you ALWAYS have to rack the slide to chamber the first round. The trigger cannot do this.