The outcome of Ch 4 will depend on a number of things. High anarchy will mean the Archon can afford to send fewer troops after you; high notoriety will mean that she sends as many as she can afford. High morale will mean your outlaws stay with you rather than melting into the woods. High leadership for (and relationship with) your various deputies will affect both what it’s possible to choose and how well your outlaws perform under those leaders. If you’ve inadvertently made a Laconnier friend, he’ll find a way to get you some rather useful mage-forged lances. And so on.
That said, your stats will also matter, and beating the Archon’s troops in the field is by far the dumbest hardest way through Ch 4. Doing it with a 0 COM should be impossible, and with a 1 COM very, very difficult.