Not necessary, see the original paper.
For example, SECDED (single error-correction, double error- detection) can correct only a single-bit error within a 64-bit word. If a word contains two victims, however, SECDED cannot correct the resulting double-bit error. And for three or more victims, SECDED cannot even detect the multi-bit er- ror, leading to silent data corruption.
Edit: link http://users.ece.cmu.edu/~yoonguk/papers/kim-isca14.pdf