No, the tax-free growth is a second order effect.... with the benefit being avoiding taxes on future income from the taxable account money used to pay taxes.
Let's first take an example where the tax rate is the same to isolate this second order effect. Joe has $50k in a tIRA and $11k in a taxable account. His marginal tax rate is 22% and we'll use a time horizon of 10 years and a total return of 7%.
Option 1: Joe converts to a Roth and pays the $11k in tax, ending up with $50k in the Roth. In 10 years, the Roth is worth $98,358 ($50k*(1+7%)^10).
Option 2: Joe stands pat. The $50k grows to $98,358 and is the withdrawn, at which point $21,369 ($98,358*22%) of tax is due. The $11k taxable fund has grown to $18,718 ($11k*(1+(7%*(1-22%)))^10). After the withdrawal and paying of taxes, Joe has $95,707 to spend....$2,651 less than Option 1.
The $2,651 is the amount of taxes paid over the 10 years on the taxable account returns... and is the difference between the growth of $11k with no taxes to $21,369 ($11k*(1+7%)^10) and to $18,718 with taxes ($11k*(1+(7%*(1-22%)))^10).
So now, let's add a twist that the marginal tax rate is 22% but jumps to 24% at the end of 10 years because Joe starts SS.
Option 1: Joe converts to a Roth and pays the $11k in tax, ending up with $50k in the Roth. In 10 years, the Roth is worth $98,358 ($50k*(1+7%)^10).
Option 2:Joe stands pat. The $50k grows to $98,358 and is the withdrawn, at which point $23,606 ($98,358*24%) of tax is due. The $11k taxable fund has grown to $18,718 ($11k*(1+(7%*(1-22%)))^10). After the withdrawal and paying of taxes, Joe has $93,470 to spend....$4,888 less than option 1... $2,651 due to taxes on the taxable account and $2,237 due to the increase in the marginal tax rate from 22% to 24%.
However, if one is looking at a 10% difference in marginal tax rates like between 12% and 22%, then the benefit of the lower tax rate is huge and overwhelms the benefit of not paying taxes on income from money used to pay the taxes.