Yes, kind of.
The police will tell you it doesn't, and I don't recommend you drink and drive, but....
If you think it is sobering you up, then it will to some extent. This is the think-drink effect in reverse. If you have a drink, followed by a coffee, and you think it is lessening the effect of the drink, then the drink will make you less drunk. Fact.
Sobers you up from what? From a state of drunkenness? What is a state of drunkenness? It's a psychological concept, tying together poor judgement, coordination impairment, increased reaction times. It is related to blood alcohol content, but different blood alcohol contents will lead to different levels of drunkenness in people, so psychometric measures are the only real test...
So...if this is the case...even though your blood alcohol level stays approximately the same after a couple of cups of coffee, your drunkenness MUST change: the factors mentioned above that define drunkenness are almost all affected by caffeine: it's a well known cognitive enhancer, affecting alertness and reaction time. But not your ability to stop pulling the wrong person. Allegedly.