Only if they try to identify it using the method that we apparently really don't want them to use: trial-and-error.
Absolutely every other solution at their disposal to identify the cursed ring leads to no Gotcha at all.
I guess this could lead to the PCs deciding to never trust anyone again, but that seems like an overreaction.
It leads to the PCs learning "If we do things the DM doesn't expect/like we get punished." Then the game becomes less about "figuring out how to solve problems" and more about "figuring out what solutions the DM would approve of."
If you want to discourage them from solving the problem in a creative way you don't like, remove the problem and let all magic items be instantly identified. Don't give the players a problem, then punish them when they take a solution you don't like, ESPECIALLY if that's your idea of "teaching them." Ye gods. Talk about betraying your players.