Absolutely... And you don't even have to be a 1K (though it helps).

I can't count the number of times I've called UA Reservations (and CO before then) with a "Hi I'm [location/on flight # in the penalty box] and it looks like I'm likely to disconnect in [city] because of [reason]. Are there any options for protection?"

A few times I've had airport (check-in) agents proactively book protection when the originating flight already has a delay posted.

In theory thus should be happening automatically -- or at least that's the implication -- several times I've been looking at my itinerary online or in the app and received a message similar to "One or more of your flights is delayed. You're still confirmed on your original flights, but we've also confirmed you on a later flight." -- though each time that's been a lie, either because there are no other flights available, or because it's a one-flight itinerary.