OK, not sure if you're talking about the video or a personal encounter in either a light plane or commercial flight.
In the video, you're showing a high by-pass fan with definitely damaged inlet vanes. There very well could be some compressor blades damaged from ingesting the bird itself and pieces from the inlet vanes. A good majority of the "FOD" will have been ejected in the by-pass airflow. Compressor stall is a possibility for sure, but that would depend on the extent of the interior damage. The power turbine section could be damaged and may not, so only a detailed inspection will tell you that. Serious compressor stalls can actually damage engine mounts and maybe wing or fuselage attachment points and structure itself.
I experienced compressor stalls in a UH-1 that literally twisted the tail boom, damaged the tail boom attachment points on the main airframe, and damaged the transmission, 42 & 90 gearboxes, tail rotor blades. The fireball out of the exhaust burn paint all the way to the stinger. We landed safely but the bird had to be brought to the hanger by trailer.