Actually, you will notice a difference, because your current processor is limiting the FSB at 400, which means your ram is probably running at ddr266, with the 4:5 FSB to RAM divider. This was the case with my old P4 northwood 2ghz. I recently acquired a free P4 socket LGA775 Pentium 515 2.93ghz 533 FSB from my clanmate in the UK. I had to buy a new motherboard to use it, but I bought one that uses socket 775 with DDR and AGP, so I could use my old parts still.
Anyways, I noticed a big difference in BF2 right away, because of the increased FSB speed, which also increased the RAM speed. Curious to see how much more I could squeeze out of the cpu and ram, I overclocked it up to 3.41ghz with my zalman AlCu heatsink, which raised the FSB to 620mhz and puts my ram almost right where it should be, at DDR388. This resulted in a HUGE fps difference when I was playing bf2. I used to get stutters and slowdowns all the time when playing with medium settings and no dynamic shadows and low dynamic lighting on my old 2.0ghz northwood with 9700pro and 1gig corsair (which was only running at ddr266 due to the fsb). After putting in the new motherboard with the 2.93ghz oced to 3.41ghz, my frame rate seems to have nearly doubled, it runs at a MINIMUM of 50 fps at all times, 90% of the time it is over 80fps.
I'm sure you could OC the celeron a bit to get more bang for your buck, and your old northwood heatsink will probably work fine, shouldn't have to upgrade it. I'm just not sure about the 256kb cache, other than that I would say go for it. The cache is the only real difference between the celeron and my oced p4, and our old cpus are fairly similar (although yours is a little faster), as I'm assuming there is a bit of room for ocing the celeron, so I am thinking you would indeed benefit from the improved FSB speed and DDR speed, not to mention clockspeed, if you overclock a little bit.
However, if you can afford it, I would say just get a cheap LGA775 p4 like I got from my friend, buy the motherboard I got and use all of your old parts, no need to buy new ram or videocard.
http://www.newegg.com/product/product.asp?item=N82E16813136156
After doing this, my old system feels about twice as fast in everything I do, even non-gaming tasks.