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 For the most part, wizardingWizarding 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. The Ministry does have a Department of International Magic Cooperation, the duties of which are listed on the Harry Potter Wiki:
to set standards for trade, create regulations for things like cauldron thickness, interpret international magical law, work with Department of Magical Games and Sports on the Triwizard Tournament, be present at the International Confederation of Wizards, British Seats.
There is no mention of coopoeration for emergencies, disasters, or war. In her entry on Pottermore regarding MACUSA's history, Rowling writes that during the American RevolutionWar for Independence wizards debated whether to join the wartheir countrymen or not. MACUSA contacted the British Ministry:
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 British wizards, 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 tryingCountries will collaborate to maintain secrecy. Apart from that or play Quidditch, it's every country for themselvesbut when it comes to war Britain was on its own.