If we assume correctly that he is using a 400MHz G4 machine from his sig, and that he's going to be upgrading to a 1GHz processor, then RAM or not, hard drive or not, the startup time will be vastly improved.
You're speaking hypothetically, Lycander -- hypothetically, if the hard drive was slow enough, and your RAM was from 1982, then yes, possibly, the startup time would not benefit from a processor upgrade.
But we're talking real-world here. You most definitely will see a decrease in startup time (it'll be faster)... but, as Lycander sort-of said, if your machine supported a faster RAM type and/or you added a faster hard drive (and, possibly, a faster hard drive interface via a PCI card), then you could see an additional boost in speed.