I don't think so.
When you save a project, it saves the Project, including the kit and all patterns; it also saves the kit itself, with no patterns; and it saves any instruments you've edited, outside the kit.
It'd be nice if that were clearer, indeed.
The kits should be located in your Spark library folder. User kits are not named readably, they're just named with numbers (in the file structure). Rather annoying if you ask me.