I do not find it impossible to run .net on GAE. At the very least, it is not possible to run something that was created from .net sources or interprets them at runtime. Just think of Ruby or Python, both work on the JVM (using JRuby and Jython). You may have to look for something like this or try to cross-compile your .net code into Java class files.
: Sun # Java?. JaCIL jsc. , , , - .