There is no evidence that the Americans were involved in either of Britain's wars. If they didn't already have their own problems to deal with, wizarding communities seem to operate in isolation. The only non-British participants in the Second War were Fleur Delacour in the Order, and Igor Karkaroff among the Death Eaters.
In her entry on Pottermore regarding MACUSA's history, Rowling writes that during the American Revolution wizards debated whether to join the war or not:
Messengers were sent to the Ministry of Magic in London to ask whether they intended to fight. A four-word message returned: 'Sitting this one out.' The MACUSA President McGilliguddy’s famous response was even shorter: ‘Mind you do.’
(Pottermore, Oct. 6, 2016)
This shows that some American wizards would have been willing to fight against the British, even for a Muggle war. Their loyalty was with their country, not their fellow wizards. It seems the only thing that unites the global wizarding world is trying to maintain secrecy. Apart from that, it's every country for themselves.