Agreed, it'll help but it's no guarantee.
I have way back in the day used a damaged HD to copy files from one PC to another when I had no other option. I copied the files to the HD 3 to 5 times depending on space allowed and it took forever because even during the writing process it'd hit bad sectors, then copying back I had to manually keep track of which ones failed to read and copy them from one of the duplicates. It's a total pain in the rear if it's loose files in a complex directory structure.
The next time I had that situation (yes unfortunately I had to do this sort of thing more than once), I zipped the files into one larger file and then copied it multiple times. Good news was it was less trouble to see if it worked, bad news was it's all or nothing a corrupted zip file gives you nothing usefull. I had to switch to multiple smaller zip files.
Of course now days I'd use 7zip instead of pkzip but more importantly I'd consider copying to the disk, burning a CD, and even storing on a $5 usb flash drive (4GB). Each has a different failure mode if you do all 3 maybe one will survive when the other doesn't.