I wouldn't ask the gate agent to call ahead to the next gate. If you're in the front of the plane, organized and you can deplane and start walking in the direction of the central area. You can check the monitors on the way for the exact gate for the CHS flight. By stopping to ask the agent to call, you're wasting time. Not only that, you'll likely be met with ONE agent who is assiting with connections. They cannot, unfortunately take the time to call ahead to the gate for you. The computer system NWA (and Airlink) uses in the hubs actually gives the agent a clear picture of who is on their flight and where they're coming from. It's quite simple actually. If you're not there a good agent will see your name still on the list (that's how they know who to page) and querry the flight status of your inbound flight. So, without calling ahead, they already presume you're on your way.
I agree with part of your post, but not all.
I agree not to ask the GA at the gate where your first flight arrives...as AZJ states, he/she will probably be solo at the time and focused on providing the disembarking passengers their connecting gate info.
Where I disagree is where the connecting flight's GA will "presume you're on your way". Nope, I wouldn't presume that...in fact, I wouldn't presume ANYTHING at ANY time during the flight experience in overworked 2008. GAs *can* and *will* close doors on a flight even when the computer screen clearly shows tight connecting passengers if they're under marching orders from Station Ops to get planes off on time no matter what. (Trust me, my Platinum a$$ has been left standing upon missing my connection by LESS THAN 5 MINUTES multiple times, even when the GAs see my name and status right there on their screens.)
Instead, I would agree with others who suggested having one member of your party run ahead to the connecting flight gate to stall for time while your slower members lag behind. While the runner is running, he/she should be glancing at gates that he/she is passing, and when he/she spots a GA (any GA) who appears to be idle, stop for exactly 20 SECONDS and ask *that* GA to call ahead to your connecting gate and indicate specifically that "there's a group of runners on the way". In other words, the FAST exchange should go EXACTLY like this: <While panting for breath in an obvious hurry> "Excuse me, would you please do me a huge favor? Could you please call ahead to gate <gate#> and tell the gate agent that a group of <#> runners is on the way right now? Thank you SO much!" and then move along. It is KEY to be obviously rushing, and it is KEY to use the insider term "runners" to indicate that you obviously know the drill.
The 20 seconds won't make the diff between making it or not, but the call that the one GA makes for you to the other MIGHT. I have used this technique several times successfully in the past on tight connections...the GA at the connecting gate, when I have arrived utterly out of breath, has told me "Oh yeah, gate <gate#> called me and told me you were running."