CA is Cyanoacrylate glue. This is what Krazy glue or Super glue is. The bond strength is quite high in tension, but not very strong in shear. A lot of people think it is good as a way to stabilize porous or punky wood. But there are better products. It doesn't really penetrate very deep even with the very thinned versions. If rocky mtn bill had it go all the way through a blank, there was a crack that it flowed through. And once it sets up (pretty quickly) it acts as an effective sealer preventing any further penetration from successive applications.
The Minwax wood hardener is a better product for the purpose of strengthening wood which may have damage from oiling, or even damage from agressive use of harsh solvents used to remove oil. Some woodworkers use it in vacuum chambers to get it to penetrate deep into punky or spalted wood. Any CA, wood hardener, or epoxy that is applied to exposed surfaces of a stock is going to act as a sealer that will affect the appearance of staining or final finish.