Actually, push can save you battery life. It depends on the volume of mail you get.

A family member actually gets longer battery life by enabling push and changing the fetch to 1-hour intervals instead of disabling push and fetching every 15 minutes.

Why?

The family member doesn't get many emails (it's a low-volume personal account). Fetching every 15 minutes results in 96 mail-checks per day. Conversely, assuming the family member receives 5 emails per day (and even that's sometimes generous), using the push + 1 hour strategy means the mail is only being checked 29 times per day. (It would actually be possible to turn fetching off completely, in which case the email account would be checked 5 times per day, whenever it receives a push notification of a new email, but with the Exchange ActiveSync technology not being perfectly reliable, I'm much more comfortable with a backup of once-an-hour checking to keep the ActiveSync connection alive or re-establish it if it closes.)

It doesn't sound like much, but it has a noticeable effect on battery life. A push-only account with fetch turned completely off that never receives any email should have a completely negligible effect on battery life. The tiny heartbeat that keeps the connection alive (every, what, 20 minutes or so?) is so small--just a few IP packets--that it probably doesn't even register as a single percentage point of the battery's life over the course of a day. A push account only uses more power when it receives an email.

Conversely, push on my phone actually eats up more battery life, because I receive about 60 emails per day on my push account, PLUS I have the phone set to fetch every 15 minutes (for my non-push accounts, of which I have 7). That means my phone is checking mail 828 times per day. Even then, left untouched, it still only eats through about 20-30% of the battery in a day, but combined with my actual (nearly constant) use, I usually end the day with about 20% of the battery remaining. If I turned push off, I'd see 60 fewer mail checks (which isn't much less).

Someone who receives several hundred emails per day on their push account could see their battery meter draining before their eyes.

But the act of enabling push in and of itself does not eat up more power. It's dependent on your other settings (whether you can lower your fetch interval) and how many emails you get on the push account.