I hit a cattle egret with an A-10 in training. They are bit larger than a warblers, more like 4 POUNDS.
Right after liftoff, the bird almost hit the canopy, but did an emergency slice back (roll 135 degrees and pull, sort of a downward chandelle), but managed to then hit the slat between the fuselage and gear pod. I could see the imprint of the bird. Hmm, the slat exists to smooth airflow into the engine at high AOA, like take off. So I figured the bird went into the right engine.
The only engine gauge anomaly was that the right fan speed was 2 - 3% below the left engine at the same core speed.
Went around the pattern, using a single engine profile, just in case and landed no problem.
the bird had gone through the engine. The lower fan speed was due to back pressure as the bird had foldup up the sheet metal into the fan dust about 1/4 of the circumference. And the seam where the panel opens, looked like it had a feather skirt, as the bird feathers were sticking out of the seam.
Total damage was two fan blades and some sheet metal.