No, S Pass or Work Permit holders are not allowed to be shareholder, or to own or manage any business in Singapore.
Therefore, they cannot register themselves as sole-proprietors, partners, directors or secretaries of any Singapore-registered company with the Accounting and Corporate Regulatory Authority (ACRA).
If they do so, they will have infringed the Conditions of S Pass and Work Permit and their work passes will be revoked. They will also need to serve an employment ban.
S Pass or Work Permit holders who hold the job title of "Secretary" and are not registered with the Accounting and Corporate Regulatory Authority (ACRA) are not considered to be in violation of their work pass conditions.