I've been around AA for years and years (first husband sober 37 years and I'm sober 8). Very few alcoholics get DTs, which are basically the most serious type of withdrawal, which involves hallucinations, etc. For most people, withdrawal isn't that dramatic--you feel like you've got the flu for a few days, sweats, nausea, sleep issues, etc. Even without DTs, though, withdrawal can be medically risky, because some people can experience seizures or heart issues. You can die from withdrawal without ever having DTs.
For most people, it's more helpful to think in terms of withdrawal symptoms rather than DTs. I'd say most people who are alcoholics experience some degree of withdrawal symptoms, but that isn't what determines whether someone is an alcoholic or not.