I wouldn't recommend that approach unless you are on a first-name basis with everyone at the bank & the entire police force.

I can tell you that I keep at least some twenties or a hundred in my checkbook, but that doesn't affect the balance of my checking account.
;-D

which, by the way, also varies considerably depending on how recently I've been paid. I'm a believer in the theory that checking accounts are for processing money, not storing it.