IMAP push isn’t beneficial for neither battery use or data consumption.
IMAP push, or IMAP IDLE, still requires a permanent state of
TCP connection to your email provider.
In order to keep that connection from failing, the e-mail client, MailWise, needs to send periodical keep-alive packets. Otherwise your carrier or Internet router will drop the connection.
That said, there is no way of telling in general whether pull or push is more efficient. It depends on a number of variables:
- Stability of your Internet connection (the less stable it
is - the more keep-alive packets are needed)
- Number of monitored folders are you monitoring (IMAP IDLE can only monitor a single folder per connection)
- Frequency of incoming Mail. For instance, if you get a lot of mail (let's say one eMail every few minutes) - IMAP IDLE (push) will always be expensive.