The device needs to be powered up to do this, but you don't (in my experience) need to make any settings changes in the device, so it shouldn't matter that the display is destroyed -- that is, if it works well enough to ring, you should be able to access and copy your files.
If the device won't mount as mass storage or media on a USB cable, you may still be able to recover photos from Android if they're stored on an SD card -- you'll just need to power down the phone and pull the SD card, then insert it in a compatible reader connected to your computer.