I've used the meet and greet which essentially allows you to bypass the line at immigration. They take you through the Citizens/Residents line instead.You still need to wait for bags, check in at Cayman Express and go through security at your own pace. There was no evidence of potential for holding a flight or expediting baggage loading. Still of value if connection is tight but, KathyV, I believe you are overestimating what this service can do for you.
I thought that @Candiru said that they held the Brac plane for them? But maybe I got that wrong.