Nope.
More seriously, if it could make Isildur invisible then it could make Frodo and Bilbo and any other hobbit who put it on invisible.
And it was a brooch, not a medallion. It's not Sauron's source of power (besides the fact that the Ring was) because Tom wouldn't want anything to do with Sauron. He's not concerned by the Ring and wouldn't bring home an evil bit of jewelry to make his wife look pretty. After all, he says to Frodo "Take off your golden ring! Your hand's more fair without it."
The knowing look was probably because he's the Eldest, there before anything else, and therefore recognized it as the trinket of a beautiful but long-dead woman.
[EDIT] Remember, Morsul himself said it's meant to be kind of silly...