Wait, your son's the anime nut and your handle is "8thMan"?
Anyway, it won't do the electric bill any good as mentioned, but the computer could care less whether it's on 24-7 or not... EXCEPT the hard drives. Presuming BitTorrent here, the constant "server like" access of this sort of downloads is pretty hard on hard drives. Not that they can't take it, but it will generally cause them to fail faster. Adequate cooling of course helps, as does allocating the entire file in advance to reduce fragmentation. The newer versions of Azureus, for example, have features to help with this--it does a lot of caching and preallocates the file to reduce the amount of seeking the drive does.
And a note on anime, for those unfamiliar with the industry: Assuming that we're talking about "legit" fansubs of as-yet-US-unlicensed anime here, and not pirated rips of US-release DVDs, then it is technically illegal, period. That said, a lot of Japanese companies tolerate it "under the table" because it frequently builds buzz for unlicensed series, and can, in some cases, increase the value of a property for US license because it's *already* popular, so you know it's going to sell well. If nothing else, it's a whole heck of a lot better than paying money for Hong Kong bootleg DVDs, which are inordinately easy to find on eBay and elsewhere.