Can you set a different email address for the automatic replies?

You can only set a sending and reply address.

The “out-of-office” automatic replies are sent automatically by either the email client of the recipient or the receiving server of the domain.
In both cases the recipient can decide himself to which address the automatic reply should be sent. This can either be the sending address or the reply address.
Usually the sending address is being used as recipient.

Unfortunately it isn’t technically possible to change this. It concerns the choice of the recipient. It’s similar to the option to whether or not showing the images immediately in an email.