Yes it is possible.
You can do it using the ereporter package that allows to receive exception reports from your application by email.
Ereporter will report two kind of exceptions:
- exceptions logged with 
logging.exception('Your handled exception') 
- any uncaught exceptions
 
To catch all the exceptions, I would create a custom BaseHandler class overriding the handle_exception() method; all your request handlers should inherit from this Base class.
Have a look to Custom Error Responses too.
Here is a simple example of BaseHandler class:
class BaseHandler(webapp.RequestHandler):
    def handle_exception(self, exception, debug_mode):
        if debug_mode:
            webapp.RequestHandler.handle_exception(self, exception, debug_mode)
        else:
            logging.exception(exception)
            self.error(500)
            self.response.out.write(template.render('templdir/error.html', {}))