I don't know if I buy it...
But in time erosion would take it's toll and all that would be left would be a huge sea covered with atols where the North American continent once stood...
It would take billons of years. lots of sandstone would be created. I would expect the sea floor however to get more variability in depth as the core cooled and the Earth takes on a hollow-prune-like structure.
I still plan to use geo-thermal heat exchange in my next house.