Yes, but. It depends upon what you want to do. If recording say a voice and guitar (24 bits/44.1kHz) without any applied effects, even the meanest of specifications will work. I have an 850 mHz(!) laptop with 1/2G of ram that can do this all day (well, until the 20G hard drive crashes!) so any processor around 1.6-2G and you are golden.
NB this applies to XP only! Win7 is not too bad, 2G ram is marginal but will work but should you be cursed with Vista not a chance IMHO.
People buy super fast i7 computers with acres of ram because they want to run a zillion track, put a verb pluggin of each one and listen whilst recording with "zero" delay and no crackles...THAT takes Deep Thought but we mortals can cope with far less horsepower. You just put the FX on later, piecemeal.
Dave.