That is incorrect. Push email doesn't constantly check inboxes. That's what polling does. Push establish a connection to the push server. Maintaining the connection doesn't use much data. When mail server have new stuff to sync, it will then notify your phone to sync them. Otherwise, not much data flow through other than the keep alive ping packs.
On the other hand, if you use timed interval polling, you will need to check the inbox of your mail box at pre-configured interval to see if there is any new mail. Each poll will consume certain amount of data as your phone needs to login, issue query, sync then log out every time.
The amount of data used in each scenario largely depends on how often you get new emails. Let's say, if you only get new emails once an hour, you will use one trip to your mail server to sync when you use push email. However, if you setup to poll mail server everything 15 minutes, you will use four trips to your mail server to sync only one mail. 3 of the trip data is wasted because there is no new email. On the other hand, if you constantly get new emails, push email will use more data because the phone get notified everytime a new email arrives.
Emails won't be a big data consumer either way. You can limit what you want to download (head only, head + body but no attachment or everything). On the other hand, using a mobile browser will use a lot more data than emails. Stream audio or video are obviously the number one data killer.