Nope. Because Charlie sees another angle here, the same bait Parson dangled in front of him before. If Ansom wins, then Charlie gets Parson and the Mathamancy Artifact. If Parson wins, Charlie gets Parson, the Mathamancy Artifact AND the Arkenpliers.
Charlie has enough Archons on the scene to take the garrison all by himself. Parson and Charlie already discussed this. Parson and Charley's original "agreement" was that if Charlie stood by and didn't interfere, then after Parson beat Ansom, GK would be even weaker from having to fight the RCC, so Charlie would be still be able to claim the garrison even after Parson "won".
If Charlie throws down with Ansom, then he loses the opportunity to get the Arkenpliers, and as Parson noted, he bit pretty hard on that bait the first time. Ansom's failing is Pride. If Charlie has a failing, it's GREED.