Is it possible to give a note a zero duration?
Umm, what are you trying to achieve? A note object will take duration unless it is a muted grace note...
May be that this seems a silly question, but when you have to aline some lyrics a non time consuming placeholder could be interesting.
Unfortunately this zero note duration, as Dulfagd names it, does not exist (yet) in Noteworthy Composer.
You can hang lyrics on a muted grace note. This will not affect playback. The lyric syllable will not highlight during playback.