Obviously, you could do the story up to that point if you weren’t terribly invested in getting it done early. More than likely, you’ll have to repeatedly load your game (to remove your bounty when you don’t obtain an herb), make it to the same region again, and hope you can grab the herb in the first place.
That’s assuming you can find the herb in the area detailed, and their spawn points are occasionally unreliable in other regions. However, if you run out of tonics that fortify your health, your horse dies, you fall, or any of the aforementioned details change as you move deeper into New Austen (early in the game), then it’s going to be that much harder to remain alive. Theoretically, you could time the shot, experiment to determine how the direction of the shot is programmed, and repeatedly fortify your health until you reach the herbs. The last implies that either the shot missed (unlikely), or the Potent Health Cure gave me the ability to take one shot (most beneficial).
The only opportunity I found with the programmed death sniper that appears when you arrive in New Austen while Blackwater is restricted, is that the shots happen at an interval, a shot hit a tree (instead of my face) when I was trying to pinpoint the direction of the shots, and I think my character reacted to a hit instead of immediately dying.