At about 18:00, when the nurse injects David with a drug of some sort, she injects it into the IV bag, however it takes effect instantaneously. Mixing a drug into a large IV bag like that would dilute any drug in that small a quantity to the point where it likely wouldn't have any effect, and would take potentially hours to be absorbed.
David's hands are bound in 'safety mittens' and he does not have access to writing materials so he could not have scrawled the illegible "note" that Kristin takes from him.