If you send e-mails and surf the web (ex. reading the news) then no.
Alot depends on what other parts you have: amount and speed of ram, harddrive(s), graphics card, etc.
Socket 478 compatible chipsets usually use AGP graphics interface so therefore it would be hard to find a decent graphics card for your old computer. And even if you found any then the pci-e variants tend to be cheaper. Most likely you would run into massive bottlenecks aswell. Socket 478 uses DDR standard memory(up to PC3200), which is really slow, even compared to slowest DDR2 standard (PC4200) memory-modules .
If you're into gaming, new games in particular, then you should.
Ulitmately, if you have around a gigabyte of ram, and do casual things with your computer, then you wont be needing to upgrade.
If you want to play games, watch hi-res movies, convert videos and such you probably should get a newer setup. Doesn't need to be an super expensive one, basically everything new(with a couple of exceptions, intel Atom, weakest Amd fusion APU's) you can get your hands on is better than that old P4 Prescott based machine.
Socket 478 uses DDR standard memory(up to PC3200), which is really slow, even compared to slowest DDR2 standard (PC4200) memory-modules .
Actually, you are right, but I would also like to mention that there are MBs with socket 478 which support DDR2 memory too (for instance, ASRock P4i945GC and many others like this one with DDR2 memory slots)