Yes, but slow.
Yes, it probably will run, but you have not provided video card info. It has to be at least DirectX 9 with WDDM 1.0 compatible. (If it worked in XP, it will probably work with Windows 7 - you just won't get the Aero features most likely). You can use a standard mode without transparency or the old "classic" mode.
Because it's a Celeron, you're going to be at a snail's pace, but you are probably already there if you are running XP.
The type of HD is also important - this is a large bottleneck that slows down an entire system. If its an IDE hard drive, again you will find it to be very slow.
With that kind of hardware, you may want to seriously consider purchasing a new computer on the cheap instead that uses a...