Not necessarily. Mine failed. It sounded like a broken timing chain and only got worse as i continued driving. Clutch would not engage but no warnings at all.
I replaced it with whatever brand water pump i could find faster cause i needed the car. The new water pump turned out to be faulty. The clutch would not engage properly resulting in no power. Again no warning lights or codes in the ecu.
Finally replaced it with a brand new vw water pump and works fine since then.
Another possible cause of power loss on low rev could be the flap controlling the compressor/turbo air flow. The motor fails, the flap is stuck.
99% of the time, it will throw an ecu code. But i cant explain the sound you can hear in this case.