No.
It's a rogue only skill and as such is only available to rogues. It does not take a trade skill slot. I have skinning and leatherworking on both my rogues AND poison. Once you do the quest, poison is a skill that's similar to the abilities other classes get with a tradeskill twist (i.e. you learn new poisons and tiers of poisons every few levels but there are skill requirements. Like, Mind-numbing poison requires 100+ poison skill AND character level 24).