If you define "sugar" as white processed sugar; and "addiction" as something that produces physical cravings than the answer is an absolute, unqualified "YES".
Of course by that definition water is also addicting (which it is). The difference is that refined Sugar has zero positive benefit to the body and causes more health problems on a wider scale than any other single substance consumed.
As others mention, naturally occurring sugars in fruits and veggies are another story.