Would greater German aggression have changed the battle?

Would the result have changed if Hitler had allowed the German surface force to act more aggressively?

Possibly at the tactical level, but a longer, harder fight would have increased the chance that HMS Anson and the distant covering force arrived and destroyed the German cruisers.

More aggressive handling might have allowed the German cruisers to inflict more damage and resist pressure from the British light cruisers and destroyers. A longer battle would also have increased the chance of HMS Anson and the distant covering force arriving. The British had more heavy ships available, so additional German sorties gave them further opportunities to engage. Fuel shortages and conservative employment limited German exposure and helped preserve a fleet in being. Aggression therefore offered a possible immediate gain at the cost of greater danger to ships Germany could ill afford to lose.