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 Core 2 Duo processor or better.
You're not going to experience Windows 7 like you see on pictures or videos online. You'll probably need to run it with the basic theme or classic theme. Once you're installed, if this does not bother you, go for it. If the computer is used primarily for work, business, or Internet (i.e. very little gaming or graphics design work) you should be OK.
If you want the full 100% experience, consider a replacement computer, since this will include Windows 7 Home Premium.
Think of your computer as a depreciating asset. With that in mind, how long can you go with this old computer? It could be a cost savings to you to buy, say, a dual-core laptop for a few hundred extra, rather than buy the software seperately. This all depends on your budget.
But it will certainly work.
Update: I am basing this under the assumption you are using a classic Intel Celeron processor and not the Celeron-D. If it is a Celeron-D with a later 965 (as it appears the 965 is capable of running games decently), than you should be very well on your way to a good install of Windows 7.