The short answer is yes. Coffee and caffeine can interfere with your performance. Whilst caffeine is a stimulant, as noted, it is also, as previously noted, a diuretic, and it changes your metabolism.
The diuretic impact could be making you tired. Insufficient hydration does make you feel tired. It could be the caffeine messing with your blood sugar levels when you are at a . . ., I forget how it is referred to at the moment, but your daily peaks and valleys of energy. For instance, drink a cup of coffee first thing in the morning, and if you normally experience an energy low around noon, the caffeine can increase that impact. I'm NOT saying it DOES, it doesn't for most people, but it CAN. It does for some people. Just how your body responds.
The best way to figure it out is to change what you are doing. Don't drink the coffee first thing. Wait until just before you start into that energy valley. Make sure you drink PLENTY of water. Try carrot juice or another juice blend. Try green tea - very little caffeine, but still hot and satisfying.
I've hit on a routine of mostly hot green tea. I save the coffee for when I really need the caffeine jolt.
You might also want to be aware of how much caffeine you truly consume. Don't forget that most sodas have tons, as do energy drinks. Guarana is caffeine (frequent ingredient for soda and energy drinks). Iced tea is made with black tea, which is higher in caffeine than green and adds to the total.
I had a friend who got nasty headaches when the doc made him cut the caffeine. He didn't think he was drinking much, until the doc added it up for him. One cup coffee, a coke or two before lunch, iced tea with lunch - with refill, etc etc . . .