Very likely. It is very likely to work. You may have some problems, see here at SevenForums.com:
Mobile Intel 965 Express Chipset Question - Windows 7 Forums 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.