Alchemy is great for a mage it helps them across all skills, but its a crutch for destruction. It is not usually a good thing for a mage to poison everything in the room and then start blasting spells, that is a good way to kill your mage.
I don't mean for the mage to poison everyone before he starts blasting away, I mean for the mage to use alchemical buffs before he starts blasting away. But when combined with effective Illusion, yes: a mage can poison someone, blast the crap out of him, and move on without anyone realizing it ever happened

Two things: 1. I find illusion to be pretty redundant with alchemy. True, both bring their own things to the table but the main reason I use illusion (invis, fury, calm) can all be achieved via alchemy. I wanted to incorporate some magic into my thief--mainly illusion and alteration--but like I said I found that I was forcing myself to switch between illusion and alchemy just so I didn't feel like I wasted perks. But by all means... tell me why you like this combo, because maybe I'm overlooking something. 2. Is reverse-pickpocket-poisoning (whatever that's called) people actually a viable way to kill? In other words, is it easy to pull off/relevant?
1. I think you are overlooking something, friend. Illusion cannot do much of what else Alchemy does, first and foremost being a source of recovery. You can restore health, stamina and magicka on the fly as well as fortify both their values and their regen rate. Alchemy can also poison enemies with weakness to element/magic, buff your resistances, and fortify all of your skills, including giving a damage buff to Destruction.
That said, if Alchemy offers everything you want out of Illusion, then you go right ahead and forego Illusion, if it pleases you. Personally, I would prefer Illusion for its own affects put into AOE (because there's no such thing as an AOE poison), as well as having more intimate control over invisibility instead of relying on finite potions. More importantly, Illusion offers Quiet Casting so that my assassinations don't alert enemies. I would still use both Illusion and Alchemy for their own merits.
2. Yes, it is a viable way to kill, and it's easy if you can sneak effectively (via Sneak or Illusion), but I would sooner use it to debuff an opponent for an assassination than to kill.
Admittedly, it has limited to use to most anyone, even a Stealth Mage (in my experience). The only character I actually used it with was a Khajiit who was unarmed, and (slightly off-topic) this is where I found a lot of problems with the game. For one thing, you can't pickpocket in combat. How is a martial artist or an expert thief supposed to make use of that mechanic if he can't disarm an Orc before his battleaxe swing connects? Also, no buffs to One Handed damage, even the vaguely-written "double backstab damage" effect, affect unarmed. As an RPG veteran, I would have thought that "backstab" meant "attack unawares from behind," especially since you can backstab with a mace

Given the length of the thread, it's likely that you missed this, but it was discussed earlier that, for this build, it's probably unwise or just not useful for mages to go around poisoning things unless they have a weapon. Carrying a dagger or bow, poisoning an enemy, buffing yourself and switching to a powerful Destruction spell can all happen rather quickly, and the damage output can be enormous

But I rely solely on the buffs. I'm still considering picking up a dagger, though I kinda wish I had used Conjuration for the bow.