You might. Personally, I’ve never been asked a brainteaser in an interview for a banking position. But I’d say it’s more common for Analyst interviews than for Associate interviews. See Interviewing – Brainteasers for some common ones.
Note that you are much less likely to get the types of analytical questions or “case studies” common in consulting interviews (e.g. “how many ping pong balls fit into the Empire State Building?” or “how many gas stations are there in the United States?).