Hahaha at maxed out.
Yes, a 13+ gives you a +1, a 16+ gives you a +2, and an 18 gives you a +3.
However, these scores were generated with 3d6, in order. So, yes, if someone happened to get a 16, they would have a 15% chance at helpful (rolling a 10, 11, or 12 on 2d6)
With a d20, you always...