would an smart phone work if i put in a sim card (att) that does not have a data plan?

[osbaldo 5/22/97]

i want to get a smart phone with wi-fi and but not a new sim. i have a sim card for a phone that has no internet and i want to know if the wi-fi would work on a smart phone or if it would work at all. My friend used to have a normal phone that only had calling and txting. so he put his sim card into a smart phone and he could use the wi-fi, would this work for everyone