Sudo'ing to a user then running screen doesn't work out of the box. Typically you get the following error:
Cannot open your terminal '/dev/pts/1' - please check.
Recently I found an answer to this problem here: http://www.hjackson.org/blog/archives/2008/11/29/cannot-open-your-terminal-dev-pts-please-check
From the blog, here's the procedure
sudo su - someuserscript /dev/nullscreen
Should work now.