Dell do not use the ATX standard, and therefore no, it most likely wont be compatible and wont fit in your case.
PC Power and Cooling are the only brand i know of that make Dell compatible PSUs - and they make very, very good PSUs by the way.
Dell Upgrade Power Supplies from PC Power & Cooling
Oh and by the way, please dont double post, just use the edit button.
EDIT: Ok, just saw a link for that adaptor in the OP, so assuming it works then you can use any ATX power supply if you use that adaptor with it.