is the behaviour of the sim 737 with the limit surge stall realistic
The answer is
no for the original software sims.
But I'm not sure of the context of your question. If you are trying to get through a sim ride then I suppose you can always prepare yourself for the actual software experience in that sim. If you on the other hand are trying to prepare for a real life scenario than you should be aware of the differences between what the software/Sim hardware can deliver and what really happens.
In the original Sim configurations both the engine surge characteristics as well as the engine seizure characteristics were well off the mark of reality. With the simulated surge being benign compared to real events and the seizure being too severe. All this should have been updated in later training syllabus to follow the recomendations in this link.
http://fromtheflightdeck.com/Stories/turbofan/