Subject: what happens in a copper/zinc voltaic pile with salt water electrolyte

I understand that in a copper/zinc voltaic pile with a sulfuric acid
electrolyte, the zinc decomposes to  zinc ions (in the electrolyte) and releases
electrons, which travel through the external wire to the copper electrode. These
electrons then combine with the positive hydrogen ions in the electrolyte and
hydrogen gas is deposited at the copper electrode.

What i dont understand is how this would occur with salt water as the electrolye
(NaCl - aqeueous). I know (from research) that a voltaic pile using salt water
as the electrolyte will indeed generate electricity, however it seems unlikely
to me that pure sodium would deposit at the copper electrode (as the hydrogen
did). this seems odd to me because zinc is lower in the reduction potential
chain than sodium and so would not reduce it and also because sodium is not
something often found in its pure form.

Does some new reaction take place? what happens to the electrons and ions in
this voltaic pile? 

Re: what happens in a copper/zinc voltaic pile with salt water electrolyte