If the pump's motor truly draws zero amps (is an open circuit or "burned out") then it cannot damage the CCU. To confirm this, you should unplug the cable at the pump and put an ohmmeter across the motor terminals. A burned-out motor will read infinite ohms. To be safe, leave the cable unplugged so that the motor can't "change it's mind" and suddenly start drawing current.

If you are getting sufficient heat and don't want to bear the expense of a replacement, leave it alone. To get a little more heat, remove the dead pump and bridge the gap with a piece of pipe. If that still doesn't provide enough heat, especially around town at low engine speeds (sitting in traffic, etc.) then you must replace the pump with a good one.

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"Buster" in the '95

Our all-Diesel family
1996 E300D (W210) . .338,000 miles Wife's car
2005 E320 CDI . . 113,000 miles My car
Santa Rosa population 176,762 (2022)
Total. . . . . . . . . . . . 627,762
"Oh lord won't you buy me a Mercedes Benz."
-- Janis Joplin, October 1, 1970