If a German-Mexican military alliance had been formed during World War I, it would have had significant implications and could have altered the course of the war. Here are some potential impacts:

1. Distracting the United States: One of the main objectives of a German-Mexican alliance would have been to divert American attention and resources away from Europe. By opening up a new front against the United States, Germany could have forced the U.S. to redirect its military forces and supplies to defend its southern border, delaying or reducing its ability to provide support to the Allies in Europe.
2. Disrupting U.S. supply lines: With Mexico as a military ally, Germany could have potentially disrupted or attacked American supply lines that were crucial for supporting the Allied forces. This could have created logistical challenges for the United States and impacted their ability to sustain their troops overseas.
3. Increased pressure on the United States: If Mexico had joined the war against the United States, it would have put additional pressure on the U.S. military and government. This could have prolonged the American entry into the conflict and increased the overall strain on the U.S. war effort.
4. Heightened instability in North America: A German-Mexican military alliance could have escalated tensions and conflicts in North America. It might have fueled anti-American sentiments in Mexico and potentially led to increased border clashes and raids, resulting in further destabilization in the region.
5. Potential territorial gains for Mexico: As per the Zimmermann Telegram, Germany promised to support Mexico in reclaiming territories lost to the United States. If successful, Mexico could have regained control over regions such as Texas, New Mexico, and Arizona. This would have had long-lasting geopolitical consequences for North America.
6. Impact on European theater: Depending on the extent of Mexican involvement, a German-Mexican alliance might have forced the United States to allocate significant military resources to defend its southern border, thereby reducing its capacity to contribute to the Allied efforts in Europe. This could have affected the balance of power on the Western Front and potentially prolonged the war.

Had the alliance materialized, it would have undoubtedly had far-reaching consequences for the overall dynamics of the conflict.