Have Gmail forward incoming email to your phone as a text message (
number@messaging.sprintpcs.com)
Use program like Magicall to perform a send/receive when a text message with "Subject: " in it arrives, then have it delete that text message.
Phone will trigger a new email notification once the email is received.
This is the most battery efficient way to achieve your goal. I use this in conjuction with push email (more than one email account obviously).