Extending a pebble path for an old home
It will work as well as the previous path has.  Building the slope into the path means you don't have to worry so much about the base - one of the main reasons for a good crushed rock base is to aid in draining.  Also, this is not a large slab area - it's just a narrow path, so going with a packed dirt/clay base is fine.

In the worst case, you'll shovel it back into a mesh to separate the pebbles from the dirt, and re-lay it out later, but I expect if you follow the design of the existing path you'll be just fine.  It'll match better as well.