That depends on a lot of things. You can configure a service to be started in a certain account. Typically services are started under the LocalSystem account and do not allow any desktop interactions. But you can install the service to run under a different account and also allow it to have desktop interaction (but only if it is started under LocalSystem and only before Windows Vista).
Any executable started by a LabVIEW application through System Exe will simply inherit the account settings and permissions of the LabVIEW application. For anything else you'll have to dig into CreateProcess() and setup your own access permissions values to be passed to CreateProcess() or you can use CreateProcessAsUser() but it still requires the according user handle that you somehow have to determine and open.