I believe you can get push support through IMAPs IDLE extension, but I've had a hard time finding an IMAP server that supports it and isn't a fully fledged corporate system.
I can't pretend to know anything about IMAP or Exchange, but one would assume that push uses less than polling the email server every 5-15 minutes.
I use an Android phone and I get an email notification via text messages.
Works well in India, not so much in USA (due to the 140 char limit in Twilio, message concatenation is not allowed)
Just to put this out there, K-9 is the fork of the andriod mail client you really want to be using, it does IDLE.