Not by itself. Assess the actual managerial or executive responsibilities alongside the other L requirements. Project importance is not a substitute for the required capacity. Ask instead which party is asserting what. A company asserts that the position it offers sits in managerial or executive capacity and that a qualifying relationship exists; the applicant supplies the year of qualifying employment abroad within the preceding three years. Project leadership may be evidence toward the first assertion, but it does not discharge either party's burden on its own.
Distinguish direction from project delivery
Explain the applicant’s decisions and who performs the work. A person may coordinate an important deadline while primarily delivering operational tasks. Present the genuine duties rather than relying on the project’s size or visibility.
Hypothetical example: a general manager at a small-craft dealership spends a year abroad with a related company, then is offered a U.S. role opening a service operation. The dealership's officer describes a management position; the duty list, read closely, is mostly hands-on scheduling and customer handling.
Counsel advises the company either to staff the operation so the described authority is real, or to reconsider whether the role is managerial or executive at all. The applicant cannot repair that from their side, since capacity is a property of the position the company offers rather than of the person's ambition.