As far as I know while the Management Engine is in all chipsets that accompany Intel CPUs, Apple never shipped any AMT enabled firmware. This is the more exposed component.
The ME is most definitely there but AMT is not. And AMT is the one with far more exposed security flaws that can be exploited over the network by virtue of AMT's purpose. Like the ones detailed in the article here. Otherwise without a shadow of doubt the ME is present in every Intel chipset since 2006.
Exploiting the ME is possible even without AMT but it definitely raises the bar in the sophistication of the attack.
The me_cleaner tool might do a good job in disabling the ME in most cases but since it's doing it by removing components from the ME FW it probably doesn't work with every OEM implementation.
me_cleaner removes most of the ME code (including the HTTP parser listed here) and then causes it to crash after bringing up the system, so it's impossible to communicate with the processor running ME. That's about as good as it gets.
i have been told somewhere on the scary internet that the nature and architecture of a mac makes the ME dysfunctional because everything else is apple-made. custom chipsets and so on.