Do you play a note in the left hand if it is still "held" by the right

Question:

Do you play a note in the left hand if it is still "held" by the right hand?

In Chopins Noctorne Op 9-12 in the 12th measure the right hand plays the chord a1-f2 for 3/8 while the left hand is supposed to play three chords of eights - e-1 / e0 c1 / h0 c1 a1 - as a result for the last chord of the left hand you should play the same note (an a1) already held by the right hand - so do you even play it? If yes how are you supposed to do that? If no why is it written down?

Thanks in advance for your answers

Best Answer - Chosen by Asker: I think for fingering sake you should still do play it even though you won't necessarily see it.