Question:
Can You bentch if you threw up?
Answer:
Essentially since the food was thrown up, the person is no longer benifiting from it and there would no longer be a requirement to bentch.
Sources:
Sharei Teshuva O:CH 208-1, Shevet Halevi 1 208 (208). See Orach Yisroel (R. Grossman) 19-7 that in the rare event that he is still feels satiated after throwing up (he at a lot) then he would have to bentch.