If I am lighting the menorah in a public area, may I announce on behalf of the people [i.e. nonreligious Jews] who I suspect will not be lighting the menorah in their home that they should have a mind to fulfill their obligation with this lighting?
No, on the contrary, you should announce that nobody fulfills their obligation with this lighting and that they must re-light the candles at home. For those who don’t have candles one should distributed it to them by the occasion.
The public menorah lighting’s that take place are done for the purpose of publicizing the miracle and not for the sake of fulfilling the obligation of the masses, who remain obligated to light at home. The entire idea of lighting a public menorah comes from the post Talmudic custom of lighting the Menorah in a shul, of which the Poskim can write that nobody fulfills their obligation. The reason for this is because the mitzvah of lighting Chanukah candles was established by the sages to be done by the entrance of one’s home or within one’s home, and lightning elsewhere does not fulfill the mitzvah, just as the mitzvah of mezuzah can only be fulfilled when attached to the door of a house. For this reason, the Rebbe stated that it is proper upon lighting the public menorah for it to be announced that nobody fulfills their obligation with this lighting, that they must return home to light.
Sources: Rama 671:7; Rivash 111; Levush 671:8; Beis Yosef 671; Toras Menachem 5747 2:98