Can Coda 2 edit a file that the current user does not have permissions for?
No, it can not.  Coda 2, Coda, and Transmit all allow you to SFTP into a box, but when you try to access a file that is not in your user's accessible range, you have to log out and then log back in as a user who can.

I use Transmit and Coda 2 constantly and just have made it to where I am only signing in as root because I ended up having to log in as different users to access one file and then a different file.

I wish there was another way around it, like being able to have Transmit, Coda, or Coda 2 push some kind of command to the server or something but it isn't possible in any of the Apps current states.  I would highly recommend doing a feature request to them, I can't see how we would have been the only people who have ever wanted this.

I would recommend trying to contact them through their twitter account.  They are pretty cool guys and have responded to things like this before on Twitter.

http://twitter.com/#!/panic

I know it wasn't the answer you were probably looking for but I hope it helps.