I doubt it. The earth is like a bag of jello and if you tried to thrust it = problems even at 1/1000G, and your reaction mass could not travel through the atmosphere or it would entrain a huge volume of air, and, remember, this jet would have to exceed the escape velocity by some margin as 7 miles/second would be taken from it on it's upwards path. Lets say you make a tower above the atmosphere - say 100Km high - what you gonna build it from? The toughest known materials would slump into a puddle far below 100 Km. Even a step pyramid would not work as it would cover a huge area and cost the planetary GNP 100 or more times over.
It is OK as gedanken ware...