It is possible, but only if you start using a non-smartphone. It's not allowed if you're using a smartphone. You'd have to let att know the imei number of any non-smartphone you have for them to remove the data plan.
If you are already using a non-smartphone, just give customer care a call and they can remove it right away.
It is possible on a smartphone actually, as long as your on a mobile share plan. You will still be charged for having the plan since its required on all smartphones, but you have the option of turning it off on the myATT app on you manage your account.
*The views and opinions expressed on this forum are purely my own. Any product claim, statistic, quote, or other representation about a product or service should be verified with the manufacturer, provider, or party.