Close.  Avogadro's number is the number of atoms of Carbon-12 requried to
have a mass of exactly 12 grams.  For other elements/isotopes, the number
would be slightly different.  There is energy stored in the atomic bonds in
the nuculus, and this affects the mass of the atom according to E=mc^2.  For
example,a Helium-4 nuculus contains 2 protons and 2 neutrons, but it's mass
is slightly lighter than the sum of the 4 particles because some energy is
emitted when the particles are combined so the mass equivalence of this
energy is lost.

The reason oxygen will show up on your periodic table with an atomic weight
of 15.999 is because it's a weighted average of all the isotopes of oxygen
in the proportions they appear on Earth.  If you take a sample of oxygen, it
will have all the isotopes present in these relative quantities, so when you
go to measure it, you'll be measuring across the weighted average.

Jason

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