If you are using a VEGAS Pro version released by MAGIX, best "before" "from the VEGAS Pro Help menu [to] choose Deactivate the Software on this PC. This option can be used as often as you wish. An internet connection is required."
You can download the software "after" again using e.g. the options in sections 3 or 4 mentioned here.
I don't think that reformatting the C:\ drive will auto deactivte Vegas Pro, but when you re-install Vegas Pro, the activation process will likely consider that you have installed VP on another computer - not that this is necessarily a problem because VP can be installed on 2 devices (exception: Vegas Pro 365). Nonetheless, you can easily deactivate Vegas Pro on your MAGIX My Account and then you shouldn't have any problems when re-installing and activating VP on your new Windows 10 HDD.