If a person has net earnings over $400 from self-employment, they are required to file a federal income tax return.

Yes, they will likely be required to pay self-employment taxes.  A Roth does not reduce your taxable earnings.

But what your doing is a great idea in building for the future.  I encourage my son's to contribute to a Roth (even do a bit of matching).

https://www.irs.gov/individuals/self-employed

And for the Roth contributions to be valid, they must show earned income, thus requiring the tax returns.

With no W-2 income, because a Roth contribution of $600 requires having net profit from self-employment of more than $600 and net profit of more than $600 requires filing a tax return, a Roth contribution of $600 (which will be reported by the custodian to the IRS on a Form 5498) with no tax return filed implies that either the Roth contribution is an excess contribution or that the individual has under-reported self-employment income that is subject to self-employment taxes.