It won't be "Push Mail", but yes, you can use the Mail application and have it set to refresh/check for new mail ever couple of minutes (not sure exactly how many). One problem with gmail and the Mail application (any, not just with the iPhone) is that there is no way to apply gmail "Labels" to the messages. You can put the messages into Folders that you make on the iPhone, but it won't "sync" with the gmail on the web.
I personally prefer just to go to the mobile web version of gmail as I don't feel it necessary to be alerted when I get an email (that's what I use IM for) and that way I get all the gmail exclusive features like Labels.