Yeah sure, there are physical limits, and doing things like mining, manufacturing, and logistics are really slow compared to just thinking. But that's just time and money. I don't see why it wouldn't happen. You build a machine to make machines. First you have 1, then 2, then 4, then 8, then 16 etc.

Then when the earth is used up, you look at space. Space travel is a lot easier because you don't need to keep a meat bag alive.