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.
A portion of earnings withheld by an employer or put into a retirement plan for distribution to the employee at a later date. If certain legal requirements are met, the deferred amount is not taxable until actually paid, for example, after retirement.