No, you can only get an answer up to the limit imposed by the fact that the coastline is actually composed of atoms. The fact that a coastline looks like a fractal is misleading. It makes us forget that just like everything else it's fundamentally discrete.
This has always bugged me as a case of especially sloppy extrapolation.
The island of knowledge is composed of atoms? The shoreline of wonder is not a fractal?
Here's the new thread for posting quotes, with the usual rules: