Short answer: No you can't change that.
Long answer: create an Enemy script for all Enemy Defs and OnTick check if their mode state == 30 (Reaction FallDown (Tranqulized anim start)) and try setting the mode time to 0 until you want them to wake up. If that doesn't work try checking if their mode state is not 30 then set it back to 30 until you want them to wake up. A list of all the modes states and other info can be found in my script api help file.
Very long answer: you have to make the tranq gun not fire that particle Type, and fire your own custom one. Then in script check if the ai was hit by your particle type and make them go into their sleep animation and then pause the animation until there done sleeping. You'll also need to disable the kEnemyAIComponent while sleeping.
Download this for a list of all the script classes and functions. It'll help show you what you can change from script.
Turok 2 Scripting API:
https://www.dropbox.com/s/oyff8tb6z9klsgm/Turok2API.zip?dl=0Download Fireseed to edit animation/skinned mesh data, or import/export static meshes.
Fireseed:
https://www.turokforums.com/index.php?topic=388.0While this is intended for Turok 1, Turok 2 is almost exactly the same for particles. So checking out smoke39's guide would help for particles. And also just open some existing particles in the games particle folder for examples.
smoke39 Turok 1 Fx Guide:
https://smoke39.github.io/turok/fx.html