Actually no. All accounts are monitored for "appropriate" transactions so if anything is "out of the ordinary" it will get flagged. Cash transactions are always suspicious so this type of transaction would be an easy one. Any teller should be asking the correct questions, and if not at that level, then the computer monitoring systems would flag. Patterns of behaviour are monitored. We call it "Know Your Customer". So even small suspicious transactions should and will be caught. Basically the bank will insist on knowing where the money came from, what its being used for and where its going.
When it comes to money laundering, financial institutions are basically the eyes, ears and mouth in reporting criminal activity. And if the FIs fail to do so, they are served very stiff fines by FINTRAC. This one of the most important and costly responsibilities of financial institutions. Its part of international attack against "proceeds to crime" and "terrorist financing".
So, remember the Teller asking you all those questions isn't doing it just to be friendly! They are trained and qualified to monitor, identify and report any suspicious transaction. The compliance manager will then determine, based on FINTRAC reporting requirements, next steps.
