No. Pro rata is Latin for “in proportion.” It’s one dollar for one dollar. If you add $7k to your tIRA to do the backdoor Roth, you also must convert $7k of existing funds which becomes taxable income. So you pay your marginal tax rate, on half the amount.

IMO not that big of a deal to contribute $7k, convert $7k, and pay $2-3k in taxes to get $14k in the Roth space that will grow tax free forever. Most people are too pre-tax heavy in their retirement strategies anyway.

I'm not familiar with the strategy you're describing, but this is not how it works for the majority of backdoor Roth contributors.

If you have $100k pre-tax in a trad IRA, contribute 7k after tax for the purpose of rolling into a Roth, then you will owe income tax on the proportion of 100/107*7k, or $6,542.

You're still limited to 7k annual (for 2025) so the 14k you describe must be something else.