Seems a lot of people are confused by the Push term. One easy way to tell is if it's not instant it's not push. Read this for more info
Apple - Support - Discussions - Push vs Fetch - the facts instead of ...
For a fact gmail is not push and you can check this by going to...
Settings > Fetch New Data > Advanced
You will see here if you have an exchange or yahoo account that it says "Push", but the gmail will shows Fetch or Manual. If you go into the options you will see gmail doesn't even have the option to put it on push.