If you have another meaty food that will fit through the tip of the syringe, then by all means... But no flake or pellet.
Just FYI...
When a coral starts to become starved, you will see feeders, but they will not be at all sticky.
When it really gets bad, it stops extending the feeders at all, which is what yours has done. You are getting food into him and he will very quickly become healthy again. Within 2 weeks you should be able to feed him right in the tank without even turning off the powerheads! You can, and probably should, but you don't have to!
I would take him out and feed him this way, depending on your schedule, at least once an evening for 4 evenings... Or every other, for at least 4 feedings, then you can ignore him for a few days and soon you will see those feeders come out.