Why be roundabout? Here's the URL for the users guides for the T200. (Dunno why there seem to be two versions of the guide.)
http://www.sonyericsson.com/spg.jsp?cc=us&...=ps1_1&pid=9975
They don't outright say you have to have the SIM in to charge the phone, but they show the SIM being put in place before the charging.
(As Stan says, though, nothing about how to get the cover off. They obviously assume that's easy! Ha! It looks like there's a latch button about 1/3 of the way down the back--the sliding cover Stan refers to.)
Good luck.
Marc