The Zimmerman telegram was at most a side issue in World War I. Escalation of the German war on shipping to Great Britain and France, Anglophilia among President Wilson's advisers and the American press's siding with the Allied powers were all much more consequential causes of American entry into World War I than the Zimmerman telegram.
Before the telegram and LONG before US entry into World War I, US troops had already entered Mexico under the command of "Black Jack" Pershing (and his young protege, Lieutenant George Patton) to track down and kill Pancho Villa and his gang of bandits.
World War I was long underway before America even came close to entering the war; the Zimmerman telegram had only limited influence on the course of the war.