No. The conversion triggers taxable income (the full amount of what’s in the traditional IRA if no nondeductible contributions were ever made). But the mere fact that the original contributions were based on earned income does not make the conversion income into earned income.
Payments within one tax year of the entire amount due to a participant in a qualified retirement plan. Qualifying lump sums may be directly rolled over tax free, or, in some cases, are eligible for current tax under a favorable averaging method.