Will a strong electrolyte also be a strong acid?

No. A strong electrolyte is any substance that completely dissolves in water. Because a strong acid completely dissociates in water, it is a strong electrolyte, but the opposite is not necessarily true. For example, NaCl, regular table salt, is a strong electrolyte but not a strong acid. (To test that, acids taste sour in our mouth, and since salt dissolved in water is not sour, salt, a strong electrolyte, is not an acid.)