Yes, bow hand stays ON TARGET, bow moves IN THE HAND, NOT the wrist. Wrist is pointed with the bow hand to target. Yes, the arrow starts out to the left of the target (BUT NOT THE HAND!) and then with the drawing hand moving IN towards the face, the arrow and consequently the bow will align to target.
Bow arm and bow hand stay static and on target. The drawing motion of the string arm/shoulder turns the bow AND arrow into alignment.
Arne