In the absence of evidence of widespread poison use, I'd say its a negligible factor in ancient warfare and "below the radar" in terms of the game engine, ie something that can't be meaningfully represented.

My guess is that ancient people used poisons if and when available, and maybe it even had an effect sometimes. IIRC classic sources like Suetonius attribute many political murders to poison so people back then believe them to be effecacious: its entirely likely some archers probably employed poison on their arrows. However delivery of toxins is problematic (eg the "sewage on the arrow" idea above: good luck getting a turd to balance on the arrowhead) and the lack of a chemical industry turning out consistent batches of efficacious toxin year round argues against a consistent effect on warfare.

I strongly doubt there was a widely available poison of the order of say the classic arrow poison frogs used in the Amazon (unless Thor Heyerdahl could prove frogs sailed balsa wood rafts via Greenland...). Some ancient people undoubtedly used poisons in hunting and warfare, but they also said spells to their gods and painted blue symbols on themselves to turn aside weapons.