Most likely, a coin with the wrong alloy will have the wrong weight. Simple tests like weight, magnetism, inspection for casting bubbles or seams, and a general check to see if it "looks funny" or the surfaces are off will catch a huge majority of counterfeits.
BTW, several professionals have told me that the ONLY reason they kept a magnet on their desk (up until a few years ago) was to test 1943 copper cents. Magnets became "fashionable" when the average collector realized that many recent fakes were attracted to one. IMO, ANY counterfeit I have seen that was attracted to a magnet was in a dealer's junk box because the design, weight, texture, color, etc. was a dead giveaway that the piece was junk. The uninformed are not on CT anyway. IMO, the folks buying these 1893-S and 1804 dollars are not numismatists and most couldn't tell a piece of silver foil wrapped chocolate from an actual coin BUT PLEASE, no more talk about magnets for coin authentication on CT. You guys have demonstrated that you are better than that!
Yeah, I'm sure mostly because visual inspection and weight will catch most counterfeits before the magnet becomes necessary. But, it's a simple, non-destructive test that's worth doing in some cases, such as when evaluating silver rounds or bars.