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