I don’t know if anyone else has experienced this but I tried taking one of these on my own with no trap, the parapet continuously fake ran away and then returned. I loaded over 90 tranqs in to it and it never got close to going down even on a boosted server. So use a trap, I died many times to bring you this information.
The only dino that'll agro an unconscious paracer is a Rex. So if those are taken care off and your cautious about not bringing in extra friend with you. You don't have to worry about other creature damaging your tame.