To setup your Gmail to "push" you need to do the following.
1. Setup a Yahoo! mail account
2. Once it is setup, go into your iPhone and setup your Yahoo! mail account.
3. Go into your Gmail settings to the "Pop/Forwarding" tab, and setup your Gmail to forward all messages to your Yahoo! mail account. (don't worry, forwarding sends the email and it will show up in Yahoo! as the original senders name, not your name attached to every email that was forwarded)
4. Now, any emails that are sent to your Gmail account will be "pushed" to your iPhone via the Yahoo! account.
5. Your not done yet. If you try to reply to an email from your iPhone, it attaches the yourname@yahoo.com as the sender. We want it to say yourname@gmail.com.
So go into your "settings" in the iPhone, then go to "mail", then tap on your Yahoo! account. Next tap on the "Address" field for the Yahoo! account and simply delete the yourname@yahoo.com and change it to yourname@gmail.com. Thats it.
6. Now when you respond to emails, it will appear that it was sent from your Gmail account.
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NOTE: One issue I ran into is that anything you send from your iPhone shows up in your Gmail inbox as an email from yourself. What I did was just to go back to the forwarding settings in Gmail and set your forwarded emails to automatically archive. I am trying to find a way around this.
NOTE: After making the above changes, if you try to turn off your Gmail account on the iPhone, you will not be able to send any more emails. You need to leave it on.
Hmm interesting! I will have to try this. But will the emails show up at all in my gmail account?