It doesn't seem like it'd be a problem, except for the power supply. Be sure to buy a new one with enough amperage on the 12V rail. Also, the Dell PSU is a proprietary form factor, so it wouldn't fit in a standard ATX case anyway.
There shouldn't be any problems running whatever video card you like so long as the power supply is sufficient.
Also, here's a review with some pictures of the Studio Slim's innards: http://www.desktopreview.com/default.asp?newsID=530&Review=Dell+Studio+Slim