How can I upload a static HTML to templates folder of GAE app?
No you cant if you want to store them in static storage.
You can store them somewhere non-static but you will lose the many advantages of having it as static content.
Can I upload a static HTML file to templates folder without re-deploying the app? 
Offline I create an HTML file which I want to upload to my Google app engine app,which displays the HTML as per URLs. But I don't want to deploy my site every time I am uploading a new file. 
Any suggestion would be helpful.