No. Australian complying superannuation funds, including SMSFs, are exempt from FATCA requirements.
Under the Intergovernmental Agreement with the USA that extends the U.S. Foreign Accounts Tax Compliance Act to Australia, the following are treated as Non-Reporting Australian Financial Institutions and as exempt beneficial owners for purposes of sections 1471 and 1472 of the U.S. Internal Revenue Code:
Any plan, scheme, fund, trust, or other arrangement operated principally to administer or provide pension, retirement, superannuation, or death benefits that is a superannuation entity or public sector superannuation scheme (including an exempt public sector superannuation scheme) as defined in the Superannuation Industry (Supervision) Act 1993, or a constitutionally protected fund as defined in the Income Tax Assessment Act 1997.
Under the superannuation legislation, a ‘superannuation entity’ includes an SMSF. Therefore, SMSFs are not required to report and their owners are exempt from FATCA reporting requirements.