No, choosing T-Mobile as the carrier may or may not result in an unlocked phone depending on what you are doing.
If you are going through the Apple Card Monthly installments or the iPhone Payments Program and select T-Mobile, then the iPhone will be unlocked.
It should also be unlocked if you select T-Mobile as the Payment plan option on the Apple website.

The only time it gets locked is when you choose AT&T's installment plan. Note, that this is different to selecting AT&T as your carrier when using Apple Card Monthly Installments.
When using the Apple Card Monthly Installments or the iPhone Payments Program on the Apple website, the iPhone will always be UNLOCKED.
Yes, as far as is known, you can select T-Mobile under the ACMI and then activate it with Mint once you receive it.
You will however still need to provide an active T-Mobile line during checkout.
This should not affect the line or any other device it may be attached to in any way.