Yes! They absolutely did. And they were wildly creative about it.

Some knock-offs were semi-genuine. For example, many cities minted their own version of legitimate coins, like the wildly successful Athenian Owl. They look a little weird, but they aren’t strictly counterfeit because they contained the equivalent silver content. There was no intent to deceive, but there was a desire to show that coins from your city were as good as the ones accepted in international trade.

I have one that was minted in Egypt in ancient times and it just looks a little funky. If you put it next to a real one, you can see obvious differences. https://en.wikipedia.org/wiki/Tetradrachm

Some were straight up fakes. For example, pretty much what you said. It could be a convincing looking bronze core with a light coat of silver.

To make things a bit more murky, even officially minted coins may have been debased in times of economic hardship.

A good place to start down this rabbit hole is the term “fourree” https://www.forumancientcoins.com/numiswiki/view.asp?key=Fourree

https://en.wikipedia.org/wiki/Fourrée

Modern fakes are a whole 'nother story.