Yes, if you are forming a proprietary company limited by shares (commonly a Pty Ltd company), the same person may be the company's sole member - i.e. shareholder or owner, sole director, sole company secretary.
Information Brokers refers to this type of company as a sole director company. A proprietary company limited by shares is the most common type of company and the type almost always used for the conduct of small and medium sized businesses which choose to operate as a company. Since a change in the law effective 13th March 2000, a proprietary company is no longer required to have a company secretary.