Yup, the magnet will work.
Apparently, the switch wasn't widely publicised. There was a story in NewScientist magazine, printed at around the time the British switched from bronze to plated steel coinage. A science schoolteacher was explaining to the class about magnetism, and how some metals were magnetic and others weren't. To demonstrate, he took a powerful magnet and and pulled from his pocket a 2p coin, just like he'd done in previous years in demonstrating this. On placing it next to a magnet, he was surprised and more than a little embarrassed when his "copper" coin flew to the magnet and stuck there, contrary to what he'd just predicted it wouldn't do.
Science teachers should read coin magazines more often.

Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis