Stingray supports synchronization of persistence data, so that if you are running active/active STM instances or should your cluster fail over, then any client-node persistence should be maintained. However the actual TCP connections will not be. The clients will need to reconnect.
Stingray operates as a Layer 7 proxy, and does not synchronize TCP sessions. The overhead of doing this with a Layer 7 ADC is very high, and the probability of it actually working would be quite low due to timing and race conditions. Vendors which do have synchronization typically only recommend it for simple L2-L4 services, and not where full Layer 7 ADC functions are in use.