1) The money would be income, but not compensation. IRA contributions require compensation.
2) Deductible IRA contributions have no effect on the amount of self-employment tax one owes, it only reduces the amount of income subject to ordinary income tax. The $837 is entirely self-employment tax.
If have no income subject to ordinary income tax even without the deduction for a traditional IRA contribution, it makes no sense to make a traditional IRA contribution instead of a Roth IRA contribution.
