Will Bloody Mess automatically deprive me of the highest bounties in Three-Card Bounty? It seems that exploded bodies equals destroyed heads.
In order to answer your question, you will need to know the details of the perk.
As the wiki points out there is a higher chance of dismemberment regardless of the hit location and for the quest in question, it is somewhat harder to complete as it may not leave a fully intact head on the marks' bodies, therefore forfeiting the bonus. It is recommended to either do the quest before taking the perk or to avoid excess damage.
For me, I usually will try to aim for other body parts and using low damage weapons for the final blow, this does not guarantee an intact head but it is definitely lowers the chances of the head being gibbed beyond recognition.
The wiki does recommend you to put your companions on melee to finish the bounties off so as to get an intact head, but I have not tried that method as I usually travel alone :D
So getting the Bloody Mess perk does not automatically deprives you of the bounties just lowers the chances of getting the full amount.
No, the heads will remain intact as long as you kill them by shooting them in another area of their body.