A hard drive is mechanical, there for the more wear it gets the more likely it is to fail. So yes, downloading 24/7 will take it's toll eventually, but the same goes for anything else you might do that would put load (read/write) on to the drive, say video encoding etc.
If your drive is already making strange noises, start making regular backups now. It's probably on it's way out....but that could be next week, or next year.