Power on without screen attached?

I smashed my 6. The case is bent only on one side at the volume buttons in a shallow 'v' measuring maybe 170 degrees. The phone powers on and my alarm works :/ but the screen is non-responsive (I cannot unlock the phone), although the physical buttons seem to work. I have another 6 in good, operational condition.

I'd like to connect that screen to the bent phone, not 'installing' the screen on the bent phone, and power up just long enough to get a backup. Can this be done?