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.