If it will run Vista it will run Windows 7 just as well.
I don't see any info about what CPUs will run in that system, due to it being an eMachine I'm thinking even a video card upgrade may cause issues with the power supply it would have. For what you would pay for a CPU, power supply, video card and RAM upgrade you can pretty much get a full much better system especially if building your own from parts.
Or maybe just re-use the case and get an AMD A8 CPU with a new motherboard and RAM for a few $100. Will get you a much faster system.