The maximum one-eng out altitude is FL180?
From the start of the drift down till the end you will burn a lot of fuel (remaining engine/s at MCT) and will take a long time (an hour or so from the typical cruising levels).
So probably your ceiling will be better at the end of it, but I don't know if as much as 4,000 ft.
If unable, either a decision point or an escape route must have been planed so you don't take any chances. I have seen special charts with such points and escape routes.
There are many places in the world with such MEAs. The Andes mountain range and the himalayas come to my mind.