I saw a big doe last year right after gun season that was limping. My first thought was that someone had wounded her during the season and I talked to the land owner to see if we should go after her. She said "nahhh, we call her the gimpy doe, she's been around for a few years now". So they are pretty resiliant.

But in answer to your question, yes, I would take a deer if I thought it was wounded or sick.