If the HDD is flashable, it could happen in theory.
Once upon a time in teh DOS/Win3.x days, with mostly RLL/ESDI/MFM HDDs, we had a few people bringing in systems to the shop that they said made a wierd zipping noise, then displayed all teh characters on screen falling to the bottom, then a message "byebye data" or soemthing like that, and locked up. Turning it back on resulted in either nothing after POST, or an HDD failure at POST depending on the BIOS. HDD was dead in every case. One of the techs at the time said he'd found a virus alert on a few BBS systems that mentioned similar things, and the virus was found to write data repeatedly to sector 0, head 0, cyl 0, over and over until whatever the weak link in the HDD was would fail. I never found out if that was true or not (I was in terminals and printers then, not PCs).
As for data loss, I usually have multiple copies of everything on several computers, and really important stuff uploaded to the web in various places and used to also have copies at a few friends' places (that changed after one of them used that stuff for their own purposes without notification or credit to me). But one day, Dec 7th 2007, I lost a LOT of stuff, becuase I had a whole slew of HDDs suddenly dying completely or having a lot of bad sectors. Weather had been changing then, humidity and temperature, and I suspect it had something to do with it, but I never have recovered most of that data.
It happened when I was shuffling files around from PC to PC on the network, and physically copying over to external HDDs. All this was going on at once, and in some cases there wasn't room to keep everything on a drive, and I had to *move* backups rather than *copy* them. That was what killed my stuff.
Someday I hope to find enough of the right HDD models (they are all different manufacturers/etc) to swap PCBs on them and see if that gets any of it back on the ones that just died. Spinrite saved some of the data on the bad-sector units, but one of those just plain died in the process of trying.