When the fan stops spinning the forced airflow on the heatsink will halt. The heatsink is covered so without forced airflow it won't work very well at all, it will actually trap heat because it can't radiate very well and isn't open enough for natural air convection. Basically the same thing that happens to a watercooled system when the pump fails, the heat has nowhere to go. The part will either run hot (with throttled performance) or it will overheat enough that hardware/firmware sensors will trigger a forced shutdown. Worst case extreme (all the failsafes fail catastrophically and the silicon substrate breaks) is technically possible but also extremely unlikely, not realistically worth worrying about.

Which is why enterprise-grade hardware avoids covered heatsinks and prefers industrial designs, along with redundant (and hot-swappable) fans to force continuous airflow. The downside is that they look ugly and eat power and tend to run loud, not the sort of thing most people want to have in their home computer.

The earlier iterations of Thermal Armor (circa Sabertooth Z97) did measurably improve system temps, I think they had an integrated fan.
The last iteration I'm familiar with (Maximus IX Code) didn't really impact temps either way, it was just a cool-looking decorative feature.
Like I said, it varies from product to product. If you can't compare the products directly then you have to read reviews from someone who did.

It's actually a good approach to managing temps - basically an enclosed section which keeps the main PCB cool - if there's forced airflow under the armor. It can be very useful if you have non-blower-style GPU cards or non-reference GPU cards with "improved" coolers - these tend to be designed to cool the card itself at any cost, they just push hot air off, some hot air gets expelled out of chassis but a lot of hot air just spills over the card edges and onto the motherboard (indeed, around the parts of the motherboard which need the most cooling).

So you could somehow install a fan or two (intake and exhaust) under the armor, essentially making it into a ducted airflow system. Maybe add some dust filters, lol. The downside is that anything not covered by the armor (like RAM and mobo VRM/PCH heatsinks) will also need to be given some airflow.

Or you could do what I did, just remove the whole thing, so that existing chassis fans cool the motherboard along with everything else in the compartment/system.

Overclocking does increase PCH temps if it increases PCH workload. Cards, drives, USBs, and other hardware (including ASUS chipset add-ons) all load through it, faster memory speeds and CPU clocks allow (force) more data to flow through it, it gets hotter. Maybe CPU-intensive stress like Prime95 don't have much impact on the PCH, but moving data across all the lanes and interfaces (multiple simultaneous transfers on all drives and USBs and cards, etc) does warm it up.

The horror stories about failed liquid cooling (halted pumps, leaky fittings, corroded blocks, etc) are real but I think much exaggerated. And they mainly affect DIY loops - closed-loop AIOs are basically just as watertight as sealed heatpipes, they just "never" leak unless they're somehow damaged. Stopped pumps are basically the same deal as stopped fans - they'll make your system overheat until it exceeds safe temps and forces immediate shutdown - replacing one with the other doesn't increase safety margins.

You basically can't use pure passive cooling on the PCH, it just won't be enough. So you're basically stuck with active cooling - fan, pump, or even TEC if you want a little exotic overkill - and it hardly matters if the moving parts which force airflow (across a heatsink, through the chassis, or across the rad) are located one inch away or one foot away, if they stop moving the results are the same in every instance.

So I honestly don't feel you'd gain anything from upgrading the built-in heatsink. Especially if the PCH never seems to heat up anyhow. I couldn't say if that Zalman part is compatible without physical comparisons - but it'll have to cover the same thermal contact area, have the same mating geometry, the same mounting pressure, and compatible mounting hardware as the part it's intended to replace.

I can understand your apprehension about the built-in fan dying ... even though it's extremely unlikely to cause any permanent hardware damage (other than the fan itself being dead) ... I think the best solution would be leaving it as-is, "moving the fan out" with ducting (ie: a tube connected to a fan somewhere else), or installing a waterblock specifically designed for that motherboard. Anything else is more easily answered as a "hands on" DIY make-it-work project than on the internet, unless you can find somebody else who's already figured out the specific mod for you.