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I think so... A tandem only has two wheels and one of them turns to enable the wheels to always rotate forwards. Think about trying to draw a circle with three pens stuck through a ruler, you can probably get two of the lines to match up (so in a bike the wheels would be angled differently, ie. front wheel steering*) but the third will follow a separate path and won't be moving forward but sideways as well.
In bike terms one wheel of your rigid three-wheeler would be skidding around every corner.*They don't actually follow the same track due to bicycle geometry, leaning and complex curves.
Dramatic_Hammer
Will I? I thought about this, but can't visualise quite why it is necessary; in effect I'm just making a longer bike. A tandem doesn't have any lateral flex does it (apart from what is inherent in the frame).