You're perfectly correct in that a non-planar poly can split in goofball ways, often differently in the same render if you shift the camera just a smidge (which is often a neat trick to fix the stray firefly.) In such cases, it's hard to say whether it would be more advantageous to pre-digest something into tris or not before rendering it in Poser, but holy damn that would make for one real sluggish pipeline (compose figure and scene, export as mesh, triangulate it, etc.) DS neatly ducks this quandry by allowing you to triangulate a specific mesh right there on the spot (good luck fixing a bad split on the spot though, but TBH that's uber-rare and you can sort of fix it by various means). And yes, it's there for pretty much every reason you've mentioned and more.

I don't know if Poser has anything similar built-in to pre-digest a mesh into tris, but I would hope that it does, yes?