This is expected behavior. The workaround is to use a "Signal Builder" block with an "Ideal Torque Source" to generate a impulse torque which can spin the Generic Engine to a velocity which is greater than the stall speed. If the throttle is on at this point, it will maintain the engine's velocity.
The included model called "sdl_vehicle_starter" starts from no throttle and an engine stall, applies a throttle at t = 60 seconds, and then initiates the starter motor via the Ideal Torque Source at t = 90 seconds.
NOTE: From R2013a onwards Generic Engine in SimDriveline has new feature of Idle speed control, through which the same functionality can be achieved without the additional Torque Source:
-> Idle Speed Control -> Enable idle speed controller