The main fault here is that Ansom also had to assume Webinar and Dora would be included in the Hunt. Their bonuses were surely weighed into any combat calculations Ansom ran in his head. Even if their bonuses aren't that spectacular they are reliable and would be able to give the Archons orders in the event that Jillian is croaked/captured (the latter being a very real and documented possibility).
I'm of the opinion that the Archons will not continue the mission if Jillian is incapacitated. At the very least they would have to contact Ansom for new orders. Even if they do continue the fight without Jillian, they are now missing out on the large bonus she gave.
Everything hangs on the most unstable person in the field right now regardless of what actions the Hunters take.