Was an animal sacrifice allowed to feel pain. Would it have been rejected?

Shalom, Thank you for your question. All animal sacrifices (in the Temple) were slaughtered according to the laws of Kosher slaughtering. These laws limit pain for the animal. As has been shown in numerous studies, the kosher laws enable the less painful way of killing animals. If an animal was not slaughtered in this way, it would not have been acceptable as an offering in the Temple. Blessings.