Copy files from XP to Linux -- yes. Run something in XP from Linux -- no (and vice-versa, too). You have to boot (load the operating system into memory, start it running) in order to execute operating system specific programs.
You can make it a little easier though if you can install Wine in Linux which can execute Windows programs (a limited number of Windows programs) directly from the Linux command line. See http://www.winehq.org
for more information.