Short answer: no—unless an American coin happened to be the same size and mass as the required European coin.

Pay phones need some way to distinguish between coins and slugs made of lesser metal. This was typically done by inserting a coin through a slot of proper dimensions to verify the thickness and then verifying the mass by the coin's momentum at the bottom of a rolling chute: a coin without the proper mass would fall short of the collection box and drop into the coin return slot. Vending machines also typically included a magnet to slow steel slugs, like those popped out of electrical outlets during installation, but I don't remember pay phones having that feature. In 20th century American pay phones, the coins rang a tuned bell as they went into the collection box, so that an operator who'd instructed you to deposit 80 cents for a toll call could verify that you'd dropped the proper amount into the phone. Later models sent an electronic tone so a human operator wasn't needed.

To fool the vending device, then, you'd need a coin of very similar size, thickness, and mass to the one expected by that nation's pay phones. Undoubtedly there were situations, especially in Europe, where small-value coins from one nation proved an adequate substitute for higher-value coins of another. But those would be uncommon. One significant exception would be Canadian and US coins, which have always been virtually identical, to the chagrin of phone companies and vending machine operators near the border.

Since this isn't a question with broader historical significance, it's probably best reserved for the small questions feature of /r/AskHistorians. I am also not sure what historical documentation might be available to answer this question with the authority of primary sources. Since personal recollections aren't allowed, I will add my thoughts in the form of a question:

I was an American in Dublin during the early 1980s; I found that there was no way that US coins would work in British or Irish payphones (which I used on occasion). Although I am certain the answer is yes, is that typical of elsewhere in Europe?