You betcha!  There are two scenarios where this will work for you.  Here's how to do each:

Send email to a contact and to their ContactMe profile

1. Make sure the email you're sending is from the same email address (yours) that is on your ContactMe account.
2. Make sure the email is addressed to the same email address that's on file for that contact in your database.  ContactMe will search the email for a contact name that exists in your database so that it can attach and store the email.  If no contact currently exists for that name, ContactMe will create one for you automatically!
3. Finally, BCC the email to post@contactme.com. 

Forward email from a contact to their ContactMe profile

1. Make sure the email was sent to the same email address that you have on your ContactMe account profile for yourself.
2. FORWARD the email to post@contactme.com

Here are a few neat tricks to make it easy for you:

Once in the Contact view of an individual contact, on the "Note" tab, click on the down arrow to bring up the menu for the type of note you're about to enter.  Then click on "Email", and you'll see a message pop up that reminds you of the two different ways you can attach an email to that contact (thereby storing it for future reference):

If you click on the "post@contactme.com" link, a new email will pop up (from your default email account) that is auto-populated with proper way to attach and store the email:

In addition, try clicking on the Contact's email address in the same view:

Once you click it,  you'll see the same, auto-populated email pop up: