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Indeed is one of the largest sites for job seekers found today online. In terms of posting, the information you list on the site is public knowledge for all to see. Much though would depend if your employer is taking the time to scan the site looking for potential candidates.
Indeed will allow you to keep hidden your resume as found on their blog:
Be found by employers
Indeed Resumes are visible to employers so that they can let you know about jobs you might be interested in. But Indeed keeps your private contact information safe – employers searching on Indeed Resume will not see your personal phone number or email address; if employers decide to contact you, they must do so through the Indeed email system. Your contact information will only be shared when you choose to respond to an employer. If you apply to a job using your Indeed Resume, your contact details will be shared with that employer.
If you wish to keep your entire resume hidden – click the ‘edit resume’ button located to the right of your resume, then click the ‘edit privacy settings’ link (located to the right), then click ‘private’. You can change your resume’s visibility or remove it completely at any time. To remove your resume, click the ‘delete resume’ link within the edit privacy settings area.