Is Vuex Store accessible from console or from client's browser?

Yes they can.

The invocation I use is

document.getElementsByTagName('a')[0].__vue__.$store.state

This assumes the first link has vue properties, which is almost always the case. If not, try other tags. The UI is unpleasant, but adequately self-documenting. It's a useful debugging tool and something a user could do.

Of course, a determined and skilled user could write a browser plugin to put a good UI on this. Or maybe that's what the Vue.js devtools extension for Chrome does? I haven't actually used that.

As mentioned, you can use Vue devtools in Chrome to see the store: