I've seen and heard countless times that it's taboo to, on an audition, sing a song from the show you're auditioning for.

However, I have an upcoming audition for a play that the casting notice requests actresses going for the lead to play 16 bars of a piano piece if they choose. I read the play and realized that the lead plays a specific (and somewhat recognizable) Nocturne by Chopin. I know how to play piano, and I know 16 bars of this piece, so I suppose my question is... would you recommend I play the piece that will be in the play, or should I play something else? Thank you so much in advance for your reply, and have a lovely rest of August!
Go ahead and play the Chopin piece. In case they ask, be prepared with a couple of others to play as well. Demonstrating to the auditors that you can play the piece is different than performing with a song from a play. They will likely be happy to know you indeed have the ability to satisfactorily play Chopin and will be in your favor. 
BTW, unless specified in the audition notice, it is OK to perform a song from the play for which you audition. If the auditors happen to like your rendition, it will build interest in you for the part (or another part.) If they don't like it (they might have a rather specific, preconceived notion of what the song is supposed to sound like) it might cast a bit of a shadow. If you are unsure, ask. You should always be prepared to sing an appropriate, alternate song.
What is most important is that you do not simply "sing" the song. The song is designed (usually) to propell the character development and plot along. So the song is "acted" (like dialog) - the actor must convey motivation, subplot and all those other good actorly things. Break a leg.