Oh it will hurt their draft stock tremendously. NFL execs are not stupid, for the most part. They know what someone with a quitter mentality could do to team morale and the locker room.
These execs won't say anything to stir the pot.... they'll just quietly let the players slip down in the draft.
If you're an NFL exec, you can't be an *** like me and straight up come out and say that these players are soft and potentially bad teammates. Some fans might not like that.
But NOTHING compels them to proactively spend their money drafting these kids. Kids are silently costing themselves millions.