I can't say yet. What exact power supply do you have right now? I can see that the Dell system needs a 4 pin CPU power connector, something I'm almost sure your power supply will lack. That being said, the power supply in the Dell system is high likely 250 watts. I don't think it's smart to have a CPU and a graphics card on that 250 watts. It may be possible, but I would really advise against that.
In other words, no, buying this computer probably won't work in your situation. Try to stay away from pre-built systems from companies like Dell, HP, Lenovo, etc. The parts in pre-builts are usually incompatible with self-built systems and have the bare minimum for that system to work.