If you want to execute more tasks than this, throw more cores at it.
Also the newer Volta architecture (section 3.2 in [1]) allows independent thread scheduling of threads across warps such that each thread can have its own program counter and stack.
There're certainly sync. See how barrier is used (9.7.12.1 in [1]) to synchronize threads.
[1] https://docs.nvidia.com/cuda/parallel-thread-execution/index...
Suffice to say, the Volta "Independent Thread Scheduling" is only used for compute shaders, not for vertex and pixel shaders.
You're right to note that different warps can run with different program counters, and when communicating across warps, those need synchronization. That's what those barriers are necessary for (see GroupMemoryBarrier and friends in the high-level languages). However, the definition of dFdX chosen by these languages basically requires that all threads participating in the derivative be scheduled within the same warp. dFdX will never synchronize or wait on another warp.
Most instructions have no inter-dependency between cells. These instructions can be executed by a core as fast as it can on one computing unit until an inter-dependent instruction like dFdx is encountered that requires syncing. The computing unit is put in a wait state while the core moves on to another one. When all the computing units are sync'ed up at the dFdx instruction, they're then executed by the cores batch by batch.