Further, In most situations, your NAS will be on all the time anyway (as most people don't power down their NAS appliances) and even the beefiest of consumer model Synology NAS units use significantly less power than a desktop computer.
Why use your NAS to download files? It frees your computer up so you can shut it down when you're not using it, instead of leaving it on to wait out the downloads (worrying that an automatic update or the like will screw them up).