Welcome to the TH community, starchess!
Depending on the HDD utility itself, these options are called differently. Regardless which software tool you decide to use, always make sure that you are familiar with its features and functions. Moreover, always make sure you do a backup of your data before attempting any HDD scan/diagnostics. The Write/Read test uses different, yet intensive methods to test the surface of the hard disk. Unfortunately, it could be destructive for your data and it usually permanently erases everything during the test operation. So yes, the support guys are right, you should be able to access the HDD again get your system to recognize it, once you
re-initialize it and
partition & format it from Disk Management.
As for the other HDD tool, I'd advise you to check the software developer's website. However, after selecting the "Erase" option, it would most certainly require you to reformat the hard drive again.
The best way to prevent any data-loss headaches would be to always have your most precious files backed up on at least one other storage device/drive. This way you'd still have the data stored on the other drive, in case the primary one fails. Besides, it's better to be safe than sorry, right?
Hope this was helpful. Keep me posted if you have further queries.
SuperSoph_WD