No, the word 'addicted' is overused and simplified. People are 'addicted' to chocolate, and sweets. To their loved one's kisses. That is not what it means, particularly to those that are, in fact, addicted. In everyday quaint usage it is cute. Meant to deflect accusations (internal or otherwise) of poor impulse control.

Real addiction alters body chemistry. The body doesn't simply 'acclimate'. It functionally depends on the addictive substance. Claiming a headache due to withdrawal = addiction is like saying shivering taking out the garbage in shorts during winter = warmth addiction. Not even close to going into shock and your heart stopping due to alcohol withdrawal.

Actual addiction alters mental thinking and results in negative lifestyle effects. When is the last time you sold your body for a shot of espresso? Does drinking coffee everyday cause you to avoid friends/coworkers or result in depression? Would you forget to feed your kids if the kitchen was out of teabags?

;tldr Addiction is clearly defined and caffeine is not one of the substances known to cause it. Hence why tea and coffee are served at most [Addicts] Anonymous meetings. "Like it a lot" is not the same as "addicted to".