Already a lot of discussion about this, but I'll quickly answer your question. You shouldn't be needing to use ANY consuambles in early Kara outside of optional stuff that you choose to use like an agility elixir, food, or whatever. You might need some consumables for your tank down the line for Prince Malchazaar, and it'll really be almost mandatory for Nightbane, but that's a long ways down the line.
If you're finding your whole raid having to buff up for early Kara encounters and still struggling, the issue is with your play.
Yes. The Kara thread is a bit ugly and large, and if someone has specific questions about a boss, feel free to make a comprehensive thread about that (see, e.g., our Netherspite thread, Prince, etc.). This is a really generic question that belongs in the generic Kara thread.
Another short answer before I lock it: No, Karazhan is not a consumable-fest at all. If you go in with level 70 blues and some heroic gear, you won't need them. If you go in shortly after hitting 70, you may need some.
Your healers may need some consumables to sustain along Moroes fight.
Your tank may need some consumables if you get Romulo at the Opera event.
Your DPS may need some consumables on Curator if you're having trouble keeping up with the adds.
Your healers and tank will definitely want consumables when you do Prince for the first few times.
Your whole raid will want consumables for Nightbane.
Nothing else needs them, and on many fights, they don't really help all that much.