There is no evidence that the Americans were involved in either of Britain's wars. For the most part, 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. 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 War for Independence wizards debated whether to join their 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 British wizards, even for a Muggle war. Countries will collaborate to maintain secrecy or play Quidditch, but when it comes to war Britain was on its own.