I am sorry, I can only answer you indirectly. It is possible to log in to an app on appspot.com with a Google account. You just have to do everything a browser would, including keeping some cookies and contacting several servers as they bounce you around.
I played around with this for a stillborn project a couple of months ago and ended up with a shell script that mostly runs cURL to log in. Perhaps you could take from it what you need.
#!/bin/bash
my_app="set-this-to-my-app-id"
url="http://$my_app.appspot.com"
curl= curl --cookie-jar cookies
if [ -z "$EMAIL" -o -z "$PASS" ]; then
echo -n Email:
read EMAIL
echo -n Pass:
read PASS
fi
rm -f cookies auth
echo Login
$curl https://www.google.com/accounts/ClientLogin --output auth
-d "Email=$EMAIL" -d "Passwd=$PASS"
-d accountType=HOSTED_OR_GOOGLE
-d source=$my_app
-d service=ah
. auth # XXX Be careful here. The output of the above
# command happens to be Bash syntax too!
rm -f auth
echo Logging into app and getting cookie
$curl "$url/_ah/login?continue=$url/console/&auth=$Auth"
echo
echo Example POST query
$curl -X POST --cookie cookies "$url/some/path" -d foo=bar
echo
rm -f cookies