I have years of experience with that -
YES, absolutely, you can mix up your StarSan and store it in your corny. Use it again and again, dip your racking cane and tubing into it, etc. When the pH gets above 3, or it gets cloudy, dump it and mix up another batch. Doesn't eat into the stainless, but keeps it shiny inside! I even transfer it between cornys with a little CO2 pressure, diptube to diptube, to sanitize cornys.
Other ideas for storing, conserving - use a cheap wally world spraybottle (haircare section for small ones) and keep it on hand. you want wet contact, so you don't have to "soak" everything in a tub of StarSan. A little goes a long, long way.