These fence posts are now
sunk over 4 feet in the ground.
Will it be enough to hold
back the hill from wanting to smooth out?
If it holds for just a few
years we might have enough cultivated plants with deep roots by then
that will lend a hand in keeping the terrace
in place.
Mark, your question is one of (soil) mechanics. You would have to calculate the lateral earth pressure on both the boards and the fence posts to answer it. You can find a nice introduction here.
Basically you need to know the failure plane angle (denoted by the greek small letter phi: φ) and the soil/wall friction angle (denoted by the greek small letter delta: δ). These values will depend e.g. on the type of soil, the amount of water in the soil and the amount of roots holding it together. If you look around you'll probably be able to find manuals or codes to help calculate such supports if you are so inclined.
Realize that all the forces from the soil acting on the boards have to be balanced by forces from the soil acting on the relatively small fence posts. My gut feeling would be that the posts are possibly too far apart.
This construction has at least the following failure modes;
Corrosion of the metal posts and rot of the wooden boards will decrease the performance of the support structure over time.
One important point is to make drainage holes in the boards. Otherwise you would get additional water pressure, and water makes it easier for the soil to "flow".