I wouldn't. the requirements are a 400W PSU. Granted that is the recommendation and we all know a good lower wattage PSU usually does the trick, but I wouldn't try it on a 250W. The 305W PSU the dells come with is probably the lowest I'd venture to go with some safety, but only because we know they are pretty solid.
But you can try it. haha. It will probably boot and be fine until you run a game. That is when is draws the power and who knows if it will pop your PSU. When you overload a PSU you have the possibility of taking your motherboard, videocard, CPU,memory, or any other component with it. My buddy had a PSU blow on him and it took his video card and motherboard with it. It took him a month to get it running again once he figured out what blew and go replacements......
so you ask yourself... is it worth the risk?