Your native gmail that is integrated with Android is push, not a timed sync such as "pop3" or some other implementation.
Meaning, email is "pushed" down from the gmail/google mail server ONLY when you receive new mail. This is the most energy efficient if you receive email infrequently. If you get 9,481,274,594 an hour, this would not be energy efficient.
Lastly, go to Settings, and then browse to the Battery and then check out which apps or functions are the most energy sapping. I follow Cory Streater's advice and turn off GPS and 4G almost all the time when out and about.