ARMs vary from simple microcontrollers to the SoCs used in smartphones and tablets.
The former, probably not.
The latter probably have something similar --- and they're even less publicly documented than Intel ME/AMT or AMD's equivalent.
AMD PSP it is ARM TrustZone.
An ARM CPU is just a core. SoCs probably do have this, pretty often. I know the Raspberry Pi's got a separate processor core running closed-source Broadcom software, and which has access to the system's memory.