Does the sacrificer's saying, "This is on behalf of so-and-so," at the time of slaughtering, count as verbalizing the intention?

This is not an utterance of the intention (niyyah), because the statement of the sacrificer: "This is on my behalf and on behalf of my household" is an informing of what is in his heart, not a verbalization of the intention. The intention precedes, from the moment the sacrificial animal is prepared and slaughtered.