Accessing Google Groups Services on Google Apps Script in Google App Engine?
No you can't. AS and GAE are totally different things and won't work together.
What you can really do is (abstract):

write an AS that does what you need
redirect from GAE to the AS url to make sure that the user logs-in/grants permissions.
perform what you needed to do with AS
send back the user to GAE with a bunch of parameters if you need to
I'm trying to work out if it is possible to use Google Apps Scripts inside Google App Engine?
And if there is a tutorial in doing this out there ? 
Through reading Google's App Script site I get the feeling that you can only use app scripts inside Google Apps like Drive, Docs etc? 
What I would like to do is to be able to use the Groups Service that is in GAS inside GAE to Create, delete and only show the groups that a person is in, all inside my GAE App.
Thanks