It seems unlikely that if you go to the counter at DEN as shown in your example and give them the record locator for the new flight, that they would see that you're in the middle of a different itinerary. But if you go up to the counter and just show your ID and they use it to pull up your name, then the agent might see you have two reservations. But I ask, why would you need to go to the check-in counter in DEN in the first place, if you don't have luggage to check? You'd just go to the gate of your new flight and board (assuming you printed your boarding pass at T-24 previously.)
Some of the big boys have more sophisticated computers to detect things like this if you've entered your frequent flyer number in both reservations. From what I've read on FT, they let it go unless you have a habit of doing it repeatedly. I highly doubt Frontier would spot such an action.