I hike in SNP a lot, and there isn't any requirement for a bear canister, but they do require some kind of appropriate storage- in this case either a bear hang or a canister. Since hanging is allowed (and it's usually not that hard to find a workable tree) the rangers will usually just assume that you're going to do a hang when going over the regs at the permit station. I've never seen anyone carry a bear canister.
That said, I've been there enough times that I've seen a lot of other people's campsites, and I have actually never seen anyone else hang their food (with the exception of one person who suspended a plastic grocery bag 2 feet in the air) so I'm not sure how much people actually comply with the rules. (I do, since it's not exactly the hardest requirement.)
Obviously YMMV, but given the density of the bear population, it's probably worth doing something. It's a very rare trip to SNP where I don't see a bear.