Do property values drop on real estate when a cell tower is placed in
a residential area?

Did they in the past ?
Do they now ?
Will they in the future ?

If somebody built one near me, it would miraculously get sabotaged

I would not be at all surprized if, in the near future, people went
house hunting with a microwave detector.

If the tower is in the backyard of the house in question or is a
predominant feature in the view from the house, it would naturally
have a negative impact on its value.  If the tower is nearby but can't
be seen due to trees, terrain, etc, then the effect shoud be less.