They don't know. But they do get a copy of the 1099-Q. You may or may not get an IRS inquiry. Keep good records in case you have to explain. This is nothing you can do to head off an inquiry.
When box 2 is non taxable, TurboTax will enter nothing about the 1099-Q on the actual tax forms.
On form 1099-Q, instructions to the recipient reads: "Nontaxable distributions from CESAs and QTPs are not required to be reported on your income tax return. You must determine the taxability of any distribution."
