Is it possible for this card to stop the attaching effect of the character agenda or is it unable to due to the way the card is worded?

No. The effect is a replacement effect that changes the moribund destination. The only thing you could do is to try and use a general character save to save the character to prevent it from dying in the first place. Once the character is moribund, there's really nothing you can do to prevent it.

More generally for The Iron Throne: Because of the way the Throne is worded ("...cancel a character ability just triggered ."), it is only allowed to cancel triggered effects.

The effect on a character agenda is not triggered - it happens whether anyone wants it to or not. Since it is not triggered, it is outside The Iron Throne's play restrictions and cannot be canceled.

Rule of thumb: Triggered Effects start with Bold text. So, since the charagenda abilities don't, we know they aren't triggered effects and therefore can't be stopped by the Iron Throne.