NaCl is an ionic compound. In water it dissolves completely forming ions. Since it dissolves completely forming Na^+ and Cl^- ions it is classified as a strong electrolyte.
Strong electrolytes are completely dissociated into ions in solution and conduct an electrical current strongly.
Weak electrolytes are only partly dissociated (examples are molecules like acetic acid which forms a weak electrolyte).
Nonelectrolytes do not form ions at all and do not conduct electricity in their solutions.
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No, NaCl forms sodium and chloride ions in solution, and therefore it is an electrolyte.