As the title says, can I apply obfuscation to minified code (Google Closure)?

It seems that we can not do the opposite;

Can I run a minifier such as UglifyJS or Google Closure Compiler on the obfuscated output?
No, it's not recommended and in some cases it'll break the code (such as if you enable self-defending). You can run your code through a minifier before to make sure that it removes dead code and do other optimizations, though.