No - you need to forward them one at a time to your second account - remember you can paste in (control & V) the destination address instead of typing it in each time - having copied it with Ctrl C.
Alternatively you can create a single mail to your other account and paste into it the contents the text of each message to be transferred - Copy with a Control C and Paste with a Control V.
Much better to have only one mail account unless you seek a measure of privacy one from another.
Gmail allows the forwarding of multiple messages - see the link...
http://classroom.synonym.com/forward-multiple-emails-gmail-one-time-11791.html
Some mail utilities allow you to set a rule to act on incoming messages - Outlook for instance - you can have all messages automatically forwarded to another address I believe.
Good luck..., March 2015