One important thing to recognize here... is that Ennis is crying and making himself sick because he already misses Jack so much. Artiste, this is Ennis's strong reaction to being separated from Jack at this initial stage right after Jack leaves the scene. In a way it's very romantic to witness the level of Ennis's strong emotions about Jack here. We know from Proulx's story and from story-Ennis's own comments that the reason he got sick here was regret and missing Jack or not wanting to be separated from Jack.
If Jack had come upon this scene of Ennis crying and getting sick... well, I think the story would have taken a much, much different turn. It's sort of interesting to imagine how things might have been different (it might be a good starting point for a fanfic story).
But, in the context of the movie, Jack never knows about this strong, physical reaction that Ennis has regarding Jack's departure.