It is not strictly necessary to connect nTRST to the 20-pin JTAG connector, but we recommend it as explained in the "System Design Guidelines" chapters of the Multi-ICE and RealView ICE user guides.

Multi-ICE always resets the TAP controller by both driving nTRST low and generating 5 TCK cycles with TMS high.

RealView ICE also resets the TAP controller by driving nTRST low.  In RVConfig you can also select the option "TAP reset via State Transitions" to reset the TAP controller with TCK and TMS.

The difference is that with TCK and TMS only the TAP controller is reset, while nTRST also resets the Embedded-ICE logic in the core, which clears any existing breakpoints or watchpoints. Regardless of whether nTRST is taken to a pin or not, it should always be pulsed low at power up to initialize the Embedded-ICE logic.