No, though that is a popular rumor, especially among people who are looking for any excuse to hate TSR. This incident comes out of the Indiana Jones RPG. The statement in question actually says “NAZI(TM)*; (TM) & (C) LFL 1984; *trademarks of Lucasfilm, Ltd. used under authorization.” In other words, TSR has never made any claim to a trademark on the word “Nazi,” but Lucasfilm, Ltd. has made such a claim. However, before anyone decides to start railing on Lucasfilm, realize that the trademark in question is of the word and the associated artwork. That is, there is no claim that the word “Nazi” by itself is a trademark, but there is apparently a trademark on the word when accompanyied by the specific artwork that was seen with it in that module. In any case, if you must flame someone over this issue, please take it to rec.games.frp.misc, where discussion of the Indiana Jones RPG goes, or to rec.arts.movies.starwars.*, where most discussion of Lusasfilm goes.
I am shocked to hear that TSR might have tried to trademark the word “Nazi.” It does not look usual, especially since private security companies are often hired online to protect intellectual property. It makes you wonder if this was a serious attempt or just a mistake.