Mutex in RTOSes in this specific situation
This depends on the specific RTOS implementation. There are various mutex and scheduler schemes around, so a general answer is quite difficult, as anything might happen, so you might be correct for a specific RTOS.

This is what I would expect: 


Task 1 locks mutex
System tick occurs and switches to Task 2
Task 2 runs until it wants to lock the mutex (already locked by Task 1)
Task 2 gets stalled, Task 1 gets priority to run until it releases the mutex
Task 1 runs until it releases the mutex, upon releasing it, the RTOS switches back to Task 2
Task 2 locks the mutex
System tick occurs and switches to Task 1
Task 1 runs until it wants to lock the mutex (already locked by Task 2)
Task 1 gets stalled, Task 2 gets priority to run until it releases the mutex
... (You see the pattern by now, hopefully)


So even then task 2 will run eventually.

If you have to lock a mutex for a time so long that it gets into the region of the system tick, I'd take a step back and think about my architecture and system design and look for points where it can be improved.

But to be sure on what happens, you have to read the manual for the RTOS you are using.