Yes. You can setup a particular e-mail address to act both as an e-mail auto responder as well as an e-mail forwarder. This is a good idea since e-mail sent to this particular e-mail address will both have an auto response message as well as being delivered to you.
When e-mail is sent to this particular e-mail address, the message will be forwarded to the specified mail forwarding address. At the same time, the sender of the incoming e-mail message will automatically receive an auto response.