System Restore does run in the background but not as a resident active program. A service call is made when program configuration change such as an installation occurs.
By default, XP sets the System Restore Service "rstrui.exe" to automatic. However, you will not see the rstrui.exe program in the Task Manager enabled services listing until the service is triggered via an install or manual start of the System Restore program.
When starting the System Restore program, the rstrui.exe service is listed and the system RAM resource for that service is then displayed. So, the program does run in the background but does not take up resident resources until a configuration change is made.
Monitoring the services on my XP machines during an installation/configuration change or by manually starting the program shows that the rstrui.exe program uses approx. 12MB of resource RAM but releases it immediately upon the restore point being made or the program closing.
Disabling the System Restore service does not noticeably affect performance - but forces you to manually enable the service when you want to set a restore point.
A reasonable configuration if you're concerned about any kind of performance hit is to set the service to "manual" through the Administrative Tools "Services" menu, this reduces automatic services for that program but allows you to manually start the System Restore program without having to first enable the service.
**Note that GUI functionality and effects that XP enables by default use up far more system resources than this service. GUI effects can be easily configured through XP Powertoys "XP Tweak UI" downloadable from microsoft or through the built in Advanced Performance "Visual Settings" of the System properties settings.
Hope this helps.