Yes, a context switch can definitely occur.
This is exactly why when accessing a shared resource it is important to lock it from another thread as well. When thread A has the lock, thread B cannot access the code locked.
For example if two threads run the following code:
1. lock(l);
2. -- change shared resource S here --
3. unlock(l);
A context switch can occur after step 1, but the other thread cannot hold the lock at that time, and therefore, cannot change the shared resource. If access to the shared resource on one of the threads is done without a lock - bad things can happen!
Regarding the wastefulness, yes, it is a wasteful method. This is why there are methods that try to avoid locks altogether. These methods are called lock-free, and some of them are based on strong locking services such as CAS (Compare-And-Swap) or others.