When adding/creating an email account, the following presets are available.
Exchange
MobileMe
Gmail
Yahoo Mail
AOL
If you selected the Yahoo Mail account preset when adding/creating the account, the account was created as an IMAP account with Push access available for received messages along with an option to enable or disable Push access for the account.
The data required to connect with the incoming mail server for an email account to check the incoming mail server for new messages is minute. More battery will be used the more often an account is checked for new messages, but this alone is not a significant battery drain and especially with a single email account. All server stored mailboxes with an IMAP account are not synchronized with the server when the account is checked for new messages. For example, the account's server stored Sent mailbox is not synchronized with the server until the account's Sent mailbox is selected.
Push is not a constant fetch process. With an account that supports Push access for received messages, a new message received at the incoming mail server is "pushed" to the iPhone without the account having to be checked for new messages. In theory, Push access should use less battery compared to automatically checking the account for new messages, which isn't always the case and this also depends on the time interval set for automatically checking for new messages. You can have the account automatically checked for new messages every hour.
Depending on how much data is accessed compared to the number and length of phone calls when roaming internationally, data access can be much more expensive.