Yes. Bleach (Clorox or any brand) is just plain chlorine. It generally comes in 5% concentration for regular bleach, and 6% concentration for "ultra" bleach. That means 6% chlorine (sodium hypochlorite) and 94% water.

You can go to the pool store and buy "liquid pool chlorine" - it's just bleach, but it's a higher concentration, usually 10% or 12%. But it's often much more expensive than plain old store brand bleach, and if it's been sitting on the shelf for a good while, it's probably decreased in strength.

So the answer is: feel free to use plain old bleach as a pool sanitizer. It's cheap, and it doesn't have any of the "gotchas" that using tri-chlor chlorine pucks have.