Will it work? Yes.
Will it work the way you want? Probably not.
The speed of burning is not the issue. The speed of transcoding video when backing up a DVD will be. You’ve got a very limited memory bus (66MHz) compared to today’s machines, plus a very slow processor, and a mainboard that doesn’t have an Ultra-ATA controller, and you’re probably going to have issues.
My suggestion would be to look into the following possible configurations, depending on your budget.
Super low budget config: New 100MHz/133MHz bus Socket 370 mainboard, using a 100MHz bus Celeron or P3 processor (say, 850MHz to 1GHz), keeping everything else the same. Greatly increased performance for not a lot of money. I recently bought a new-in-box good quality MSI board like this for the machine I have built for my fiancee’, with onboard ethernet and sound on Ebay for $35 plus shipping. The 1GHz Tualatin-core Celeron cost me another $40, new in retail box, also on Ebay, which meant the heatsink/fan was included. I’m running XP Pro on that box with 512MB of RAM and an 80GB Caviar SE hard disk, and it is quite smooth.
Low budget config:
Socket A mainboard, Nforce2 400 chipset. AMD Athlon XP 2500+ retail box processor. One 256MB PC-2700 memory module (two if you have the money, as the Nforce2 can do dual channel memory making it even faster). Cost is slightly more, but speed picks up considerably. If you want an inexpensive solution that is still upgradeable over time, get a mainboard with onboard video and an AGP slot too; this will allow you to use the mainboard’s video, but upgrade someday if you wish.
Transcoding on my Athlon XP 2500+ (not including burning, etc) is usually a 45 minute process with most DVD’s. If your P2-266 could do it without errors (read: dropped frames or glitches in audio/video picture and sync) it would probably take nearly a day per disc. I simply wouldn’t do it without a hardware upgrade.