Tested and it works, except the cgminer exit statistics lines above the top of the terminal get cut off and scrolling up doesn't help (it just shows the last prompt when I typed screen -r), so I can't see the entire stats printout.
First, another answer to your original post: you can log cgminer's output to a file. Here is the relevant portion of the script that I use to start cgminer:
DISPLAY=:0 cgminer -c cgminer.conf 2> logs/$now.log
It causes a log file with date and time as part of the file name to get cgminer's output.
As to the screen scrollback issue, see GNU Screen: Working with the Scrollback Buffer