This is my first attempt at growing vegetables. I put a few Jerusalem artichokes into sandy loam soil, and with very little watering they have grown like crazy. The leaves on the bottom are starting to die off, but online references say to wait until late Fall and a drop in temperatures. Should I be waiting for all of the leaves to show signs of die-off, top to bottom, and trust that the tubers will stay intact after the plant is dead/dying? Other than waiting for the leaves to die, are there any other signs that would tell me the plant is ready to harvest? Should I have been fertilizing this plant at all?

Probably around frost date will be fine.
Would guess like potatoes, that while the top is alive but yellowing it is trying to store any energy in the bulbs. Once tops are gone, can't put any more energy into bulbs/ tubers.
Dig early, they may be slightly smaller.

In my experience, digging too early results in tubers with an 'off' taste.
You can pull a plant and determine for yourself... I pulled one last week, it had tubers...

I really doubt that you are going to see much in that pot...
I've never seen shux for tubers when I attempted pot culture...

I used to grow these in wet clay... Like where you find apios vines growing naturally. They grew extremely well for me there...

I'm in dry sand now, and they grow, but don't produce well.

As far as harvest?
My experience is to wait for frost... and only dig what I'm going to eat that day. Sun chokes do not store well... better to leave them in the ground through the winter, digging as needed.