Is NaC3H3O2 covalent or ionic

The Sodium cation will bond ionically to the oxygen of the organic anion.

C3H3O2 = H2C=CH-COO^- Na^+

This substance will be sodium propenoate. (Note the spelling)

However, I think you may have the incorrect formula.

Should it be C2H3OO in which case it is CH3COO^-Na^+ ( Sodium ethanoate.

The sodium cation bonds ionically to the organic anion.

Within itself the organic anion, be it 'propenoate' or 'ethanoate' will bond covalently.