Fan Clutch Problem

I have a 1995 BMW 740iL, a couple of days ago as I drove on the interstate, I heard a loud humming sound that only got worst as I
accelerated, I thought it was the transmission, yet the gears engage correctly. So I stopped at a mechanics and he came to the conclusion that it was the fan clutch that it was locked. The question is will a bad fan clutch make a loud humming sound, it sounds as if the engine were being stressed out, yet it drives fine and the transmission is engaging correctly. Can anyone shed some light?
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