While it’s possible to align the editor view with a camera, is the reverse true?
That is, is it possible to align a camera to the current editor view?
You’re essentially asking if you can copy one camera’s viewpoint to another. No, that’s not currently possible in the Editor. Obviously, you can copy/paste position and rotation values for cameras in your scene. But those properties aren’t visible for Editor cameras of course (Top, Bottom, Left, Right, Front, Back, Perspective).
What you can do is select the Camera entity from the view menu and move the view in the editor to where you want the camera to be. I found this quite handy to help frame certain scenes. ie:
Pity. 
(For reference the equivalent in Unity is: Select Camera, click GameObject->Align With View)
Consider it a feature request. 