Does FreeRTOS support priority inversion when configured for preemptive scheduling? I was unable to find this information from FreeRTOS websites.
Priority inversion is a feature of an application using an RTOS, not a feature of an RTOS, so no RTOS 'supports' priority inversion. RTOSes do however support features such as priority inheritance and priority ceiling algorithms to minimise its effect. Literature will tell you that these algorithms remove priority inversion, which is of course a nonsense, and an inversion would have to exist already in order to trigger the algorithm. What the algorithms do do is make the inversion time bounded - best to just try and avoid the inversion in the first place though, if it is possible.
FreeRTOS mutexes (http://www.freertos.org/Real-time-embedded-RTOS-mutexes.html) use priority inheritance to time bound priority inversions.