Yes, I can tell you from personal experience that they certainly did whistle. When I was a boy I lived in Nottingham, and until May 1941 we were lucky in that, although we heard (and sometimes saw) German aircraft, they usually passed over on their way to less fortunate cities like Sheffield, Coventry or Birmingham.
But on the night of Thursday 8 May 1941, for the first (but not the last) time, Nottingham itself was the target. We were woken up by the sound of the warning sirens, but they were very quickly followed by the sound of falling bombs (including the terrifying whistling), and we were too scared to leave the house and go into our air raid shelter: we sat on the steps leading down to our cellar.
There were a lot of people killed in Nottingham that night; luckily for us we escaped unhurt, and nobody we knew was killed.
But I can tell you - nobody who has ever heard that whistling noise will ever forget it. I am nearly 81, and I was 8 at the time, and I can remember it all too well.
So why did the bombs whistle? To warn people to take shelter? Don't make me laugh - there would be no time. There is only one reason that makes sense to me - it was to scare the hell out of those beneath them, and it certainly succeeded as far as I was concerned!