Would this work?

linkbox is just a name for a custom snippet that outputs some HTML. The question I have is if MODx 0.9.6 allows for this type of approach to work (i.e., a snippet running inside of another snippet).

You can definitely run a snippet inside another snippet.
I think you need to alternate the cache status i.e.

I’m not sure what HTML you want to output inside a Wayfinder call?

http://symphonicheaven.com/ps2/abyss/other/walkthrough/

The Linkbox snippet outputs those "boxes". Basically, I would like to leverage Wayfinder to automatically create those (so I don’t have to add them when I make a new page).

Maybe you could use your snippet inside the appropriate Wayfinder &tpl chunk?