Yes, Kroil will dissolve grease. And, yes some amount will seep into the action. But fired casing and heavy grease will hold the majority in the barrel and soften the crud. If you point the barrel into your bucket and slowly eject the case the Kroil drains in to the bucket. Normally I do not remove the bolt from a lever gun when cleaning it. However, I do keep the muzzle tilted down hill and try to pull the majority of the fouling out the front. After I have finished with the barrel, I use action cleaner to flush the action without disassembly. Not a perfect system, but it works fairly well.
I have seen others turn a wooden plug and drive it into the front of the barrel, but I am afraid it would damage the rifling. That is a risk I am not willing to take.