If that was the case, we would see M2 and M3 go up, and we aren't. Depending on how you want to measure it, you could even argue they are contracting slightly.
That said, I'm not entirely sure about the definition of M2 and how that's related to 'money sitting in the bank'. M2 includes 'savings and time deposits' according to Wikipedia, but it doesn't seem to differentiate whether banks in turn lend out that deposited money or it just sits there.