Yes, you can report the $400 HSA contribution without a corrected W-2. TurboTax lets you enter employer contributions that are not reported in Box 12 of your W-2 during the HSA section. It will correctly include them on Form 8889.
However, it's best to ask for a corrected W-2 to make sure your records match what the IRS has on file. If you can't get a corrected W-2, you can enter the amount manually. It is an acceptable option, but make sure to keep your records and documentation.
