Short answer: No.
Long answer: Yes. Read below.
Copying the files, through Windows, will not work. Why? Programs are locked. Explorer prevents you from copying certain folders, and there are several mechanisms that work in the background that prevent full copies.
This and the process using Explorer will take it's time.
The most relevant part is that the bootloader (the part that actually tells to the remainder of the machine how to start the system) isn't copied, as it resides in a special part of any HDD (the MBR - Master Boot Record). You can, however, repair the bootloader with the Windows XP installation disk.
To copy the contents of a disk to another, I would use some sort of Live CD and/or some specialized software. As long as Windows itself is not running, copying all files shouldn't have any problem.
Assuming you can copy all files and repair the MBR, then the only thing stopping Windows from running could be the difference in hardware, that translates to the drivers installed in XP.