Yes, since they were 3 months old. They travel on award tickets a lot, but still, they do earn some points on paid tickets, too.

We also signed them up for Global Entry/Trusted Traveler so that we can go through the precheck line as a family. No need to remove all the bags of babymeds, food pouches, etc, in addition to the usual laptops and shampoo. This has been fabulous for faster ventures through Security. Well worth it.