Great question. The answer is No. Why? Can you imagine how the form could be used to send out spam emails to anyone in the world if you would let people send to any email address on behalf of your website?
What you can do is to prepare a list of pre-defined email addresses and make them available for the person to choose. You'll find details on how to do this using a drop-down field by going to the following page:
Hope this helps. Let me know if you have any further questions.