Interesting theory, but in order for economic growth to occur someone has to be there to buy the goods that these machines will be producing. Fewer humans alive to buy goods with fewer jobs equals a shrinking economy, regardless of how the goods are produced.
At that point we would probably start looking at other economic systems anyway.
The labor market is increasingly becoming machine-based, rather than human-based. As the number of humans drops, the number of machines grows.
We need fewer humans to maintain growth, so dropping birth rates could be a good thing, since machines require less maintenance than humans.