Should Hipper's battlecruisers have turned and fought the British force?
Short answerNo; the Germans lacked the weight of fire, and the mobile long-range engagement favored the intended strengths of the British battlecruisers.
NotesA viewer suggests that the Germans might have turned and fought given later Royal Navy battlecruiser losses at Jutland. The comparison fails because Dogger Bank involved different British ships and a free-moving engagement rather than close action with the battle fleet. The range and maneuver suited the British battlecruiser concept by letting speed and fire control matter. Hipper's ships did not possess enough weight of fire to reverse the numerical disadvantage. The answer separates the tactical conditions of Dogger Bank from the magazine disasters that dominate later memory of British battlecruisers.