I think you may be confusing two separate things: backdoor Roth contributions and the Roth pipeline.
A "backdoor Roth" contribution is when you make non-deductible contributions to a traditional IRA and then convert this amount to a Roth IRA. You do this because your income is too high to make deductible traditional IRA contributions or direct contributions to a Roth IRA. The end result of this is that you are able to put $5,500 of new money into a Roth IRA. The catch is that there is a pro-rata rule that comes into play on the conversion step where you have to look at what fraction of all your traditional IRA money is pre-tax or post-tax. For this reason, the backdoor Roth IRA can only really be accomplished when you don't already have any pre-tax traditional IRA savings.
The "Roth pipeline" is where you convert pre-tax money from traditional to Roth, paying tax on the full value in that year. Five years later, you are eligible to withdraw that amount from your Roth IRA tax-free.
In your example, if you move $200k from a traditional 401(k) to your traditional IRA, and then covert $10k to Roth, you'll pay tax on $10k, not $200k.