I could probably make the case that if people were to exclusively drink bottled water, then the reduced capacity requirement on the water system could allow for smaller diameter pipes, and so on, which could yield a net energy savings.
They certainly wouldn't make cost savings.

The cost to the consumer in England (not Britain) of one litre of tap water is 0.08 pence per litre. Bottled water, so far, can come nowhere near close to that.

As for downgrading the water system to smaller pipes to make a net energy saving, well, I imagine such a task (digging up and replacing thousands of miles of pipes) would be incredibly energy intensive, could it really reliably make a net saving? How long would it take just to break even?