According to the UFT user's guide....yes:

UFT One supports running tests from multiple instances of UFT One simultaneously on the same machine in different Windows sessions. When UFT One is launched by a different user account than the application you are testing, the following UFT One functions may behave unexpectedly:

• Recording
• Running tests
• Spy

Workaround: Launch the application through UFT One, for example, using the R & R settings.