What you suggested would not work (many of the files will be in use), but you wouldn't want to do this anyway. The thing is, everything in C:\Windows (among other folders) is already ON the new computer, and if there are parts that AREN'T, they might confuse the computer if they were there. Similarly, if you did this, you might not get all of the registry settings copied over. Without these, the computer wouldn't be set up correctly. You need to copy over the Documents and Settings (or Users) folder, and you need to reinstall all the programs. That's the only way to guarantee that everything important is copied over without ruining the brand-new computer.
If they are certain they want ALL their files, even though there geek (you) tells them this will get every file they care about and many they don't, then you should also use Multiverse IT's solution and get an enclosure to turn the old hard drive into an external one.
P.S. In our family, two of the three of us are geeks. We always have over-extensive backups whenever moving computers. We'd definitely go for the enclosure option. However, I can tell you from experience - we would NEVER use it, not even once.