Yes, plenty. However with any processor, don't try doing anything else on your computer while burning.
Same here. I have only recently (3 weeks) been able to burn anything (replaced my burner), but my system is only 1.5ghz, 512mb ram and it works fine. Just a tad on the slow side, but not too bad. I have been using AnyDVD and CloneDVD during the 21-day trial period and (knock on wood) no coasters. Have also used Shrink & DVDDecrypter, and a couple of times burned with Nero ROM. AnyDVD/CloneDVD is faster for me -- not sure why.
I hope you're sitting down as you read this....okay...I use a PIII 800 with 128 Mb and it works perfect! If I'm recoding it takes a while but if I'm just doing burns it takes about 15 - 20 minutes. Most burns are done at 4x anyway so the fastest hardware is still only burning at 4x. So, while you are chuckling at my antiquated system, the answer to your question is you have plenty of power for your DVD backup needs.