Maybe. I watched that scene again very closely and I think it was probably there to throw us off because it didn’t look like she had the cup in her posession long enough to slip it in with all eyes on her, the cup was empty at the time so nothing to conceal it in, and how would Sansa have known the incident would even happen? It seems the poisoning would most likely be pre-planned.
I don't think so--how can anyone predict the actions of Joffrey? He was such a--well, I don't like using those words.
This was a crime of opportunity, not planning.
What about the fool who came to Sansa during the incident and tried to drag her away from the scene? I don't think Tyrion had anything to do with it--it was Sansa and the fool.