But in any event: if the coffee has affected you, you're already too late. The idea is to sleep immediately after consuming your caffeine, then wake up as/before it starts to affect you. If caffeine makes you sleepy instead of wakeful, that's probably going to be less pleasant because you won't wake up refreshed.
Finally: I suspect the sleep is helping but feeling useless. Adenosine is one chemical that makes you feel sleepy, and levels are reduced while you sleep. But caffeine is an adenosine blocker, so it's going to stop you feeling that adenosine sleepiness without disposing of it. Good sleep while caffeinated is probably hard to get, but if you succeeded I expect you would lower adenosine levels, but not feel the difference until the caffeine wore off.