This is a web design and development community, so we don’t talk about desktop data loss much around here. I’ll move your thread to the computer software forum, though…
No it couldn’t, that problem can only occur if an interruption (such as power loss) happens during the Chkdsk scanning process. And Chkdsk ONLY runs either if the hard disk has suffered an integrity issue (which the OS will detect and run on boot) or if you ask the disk to run a scan (again this only happens on boot)… Chkdsk doesn’t run in the background (unless told to) and it certainly would be VERY rare for data loss to occur as the issue would have to occur when Chkdsk is trying to repair clusters on the disk. It’s not like the file system integrity is checked on a regular occasion (or while the OS is active).