"My question is..... will a bad CPS interupt fuel delivery
to the injectors."

The answer is YES, indirectly. It all begins with the CPS, as below:

1) During starter cranking, the Crank Position Sensor sends timing pulses to Ignition Control Unit (ICU)

2-a) The ICU propagates these timing pulses to the Power Stage (aka Ignition Amplifier) to initiate spark at the coil.

2-b) The ICU also propagates these pulses to the FI ECU, to allow FI operation
(no ICU pulses means no FI operation).

3) The FI ECU energizes the Fuel Relay, which has two outputs (3-b and 3-c below).

3-a) Fuel relay sends power to fuel pumps, and

3-b) also powers AMM, IAC, ECU, and Injectors (via Radio Suppression Relay)

When all these events are succesful, the engine runs until the Ignition is switched off, which in turn shuts down the FI system.

EDIT:
As long as the ignition is OFF, there's no need to disconnect the battery when swapping or testing AMM.

--
Bruce Young, '93 940-NA (current), 240s (one V8), 140s, 122s, since '63.