Small correction: You mean Triple Alliance. Axis was in WWII. Unless you're actually referring to WWII?

I'm going to vote 'yes' IF it had happened 3 or 4 decades earlier and if the German + Irish immigrant communities had been bigger, more established.

World War 1 didn't have much ideology, just a big tangle of treaties of mutual support with Nationalist ethnic identity politics to throw more 'petrol' onto the fire. Also, you have parties like the British whose real interest is seeing to it that no Continental power gets too big.

Sir Humphrey Appleby of Yes, Minister was only slightly tongue-in-cheek when he pointed out the British "have had the same foreign policy for the last 500 years - to create a disunited Europe. In that effort, we have fought with the Dutch against the Spanish, with the Germans against the French, with the French and Italians against the Germans, and with the French and Germans against the Italians." My point here would be that no permanent ethnic or ideological connection existed between any of them. They could have lined up differently if we had played the 19th C. out again. (The British Empire's Divide and Rule policy with India and Africa did not come out of thin air!)

Add to this the British and US relationship of the 19th C. In the Civil War, Britain sided with The South. So did Mexico, but that was less ideology than recent memory of the Mexican-American war.

Lots Germanic (and Irish!) immigration to the US was a factor in our neutrality to 1917, but if Germany had united a little earlier, if the ethnic mix in the US had tilted this way or that, maybe we would not actively fight the British, but the Irish + German power base could have kept us more solidly neutral.

Another alternative - if the French revolution hadn't been so bloody - if they pulled themselves together sooner, if Napoleon didn't bite off more than he could chew, they could have been the hegemonic power that Germany and Britain united against decades later.