However the sources didn't necessarily agree on how significant arming the vessels was in the German decision to stop warning merchant ships before attacking.

Part of that reason is because it's difficult to objectively quantify "significance" with historical decisions like this. We can say it was of minor importance, or very significant, but we can't really say it was about 45.5% a factor in the German Empire's decision to conduct their submarine policies.

So I'll take a bit of a middle route, in the spirit of fairness, and say that the British admiralty's decision to arm merchant vessels was a huge rationale for the German Empire to justify it's unprecedented execution of unrestricted submarine warfare, as well as one of the first major steps in the escalation of the economic war on the high seas.

The introduction of submarines into the naval war brought a huge, and untested, factor in strategic planning. The new ship of war, demonstrably able to sink vessels below the waves by the very beginning of World War One, would be one of the main points of distress by the Allied powers, specifically the British Admiralty.

Caught up in containing the German High Seas Fleet, Royal Navy resources were already beginning to stretch. As well, anti-submarine warfare was in its infancy, rudimentary technology like depth charges would be developed as the war progressed, and strategic policy like convoying would be adopted in the late period of the War. Add the fact that U-boats could conduct their stops and sinkings of merchant vessels, and then SUBMERGE to avoid detection and pursuit, and British naval leaders felt forced to turn to (still debated) questionable decisions to combat them.

Two principal decisions were later used by the German Empire as support for their decision to execute unrestricted submarine warfare. The first was the advisement of British-flagged merchant vessels to fly neutral nations' flags in known submarine waters. In order to avoid the ire of powerful neutrals like the United States, Germany had largely promised to avoid harassing neutral-flagged vessels. The British hoped that this would exploit that decision by allowing British merchants carrying war materials to avoid molestation on the basis of flag. The second decision was far more controversial, the arming of merchant vessels and the introduction of 'Q-boats', merchant ships manned by sailors with guns hidden on deck. The idea was that a German U-Boat would surface to stop the supposed merchant, or if ordered to sink on sight, surface to use the deck gun and not waste torpedoes. When spotted and determined "lured", the Q-boat would drop some sort of covering or obstruction that hid a powerful deck gun of its own, and engage the more lightly armored U-boat in a duel. In reality, the Q-boat was ineffective in sinking submarines. However, its presence, as well as British policy to advise the flying of neutral flags on non neutral vessels, provided a large base of rhetoric for the German Empire to justify and launch it's deadly submarine campaign.