Recently, I upload the web application in my local to Google App Engine
c:\LocalProject>c:\appengine-java-sdk-1.2.2\bin\appcfg.cmd update .
Unfortunately, I accidental delete the whole folder "LocalProject" in my local disk. Is it possible that I can recover all my stuff, by downloading from Google App Engine?
No. There are libraries you can include with your app to make the source code downloadable, but if you didn't do so when you uploaded your app, there's no way to download the source code.
This is what source code management systems like Subversion and Git are for. You should be using one, even for your home projects.